{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0001","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8094533c188342210a444d1663bda631f8069dd5ec31dfe0740fcc1d003201f5","family_id":"qf-density13-connectives-and-or-table","seed":202610135001,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0002","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96240ccade822b6c89f66ec5250bc78330c09afdb22ddb07382287601b0ee87b","family_id":"qf-density13-connectives-and-or-table","seed":202610135002,"semantic_template":"qf-density13-connectives-and-or-table/[[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 1, 1, 1, 1, 1]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0003","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f92b657be8c52987f22faa748fa1cf1f8acb1638ea3a356f1c8d0bc4ea3d09cf","family_id":"qf-density13-connectives-and-or-table","seed":202610135003,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0004","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3f26b2b4d54a56692100aa07480f9da04bdb17f47a3fef5fb1cdc5d108316a39","family_id":"qf-density13-connectives-and-or-table","seed":202610135004,"semantic_template":"qf-density13-connectives-and-or-table/[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([True, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0005","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5bac173e9ba94caadc3f3143935839053729773d18c468229f3269fe40155f78","family_id":"qf-density13-connectives-and-or-table","seed":202610135005,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0006","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"691e485445e7c4c47c7e79debf34f9dea04540e5f5d7151e8b5108dd829fc9a6","family_id":"qf-density13-connectives-and-or-table","seed":202610135006,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0007","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b3bdf1a12a4a28087e90141f150ba4e5f0c98b84285742f607c8ec557cb3862","family_id":"qf-density13-connectives-and-or-table","seed":202610135007,"semantic_template":"qf-density13-connectives-and-or-table/[[1,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([True, False, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0008","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"942bb4f95316a5d4aba8614980b2297484915a6111409898b5665ade3b377efd","family_id":"qf-density13-connectives-and-or-table","seed":202610135008,"semantic_template":"qf-density13-connectives-and-or-table/[[0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0009","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc3a6f824bcfa50b40f19242ef5b4459a7aa735a44e9076358c514c34d7d3dee","family_id":"qf-density13-connectives-and-or-table","seed":202610135009,"semantic_template":"qf-density13-connectives-and-or-table/[[0,1,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0010","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f1064b05b1d6cdde0e8a1c96c1e6db7f8348b3bae4f14b36f289e352678ba224","family_id":"qf-density13-connectives-and-or-table","seed":202610135010,"semantic_template":"qf-density13-connectives-and-or-table/[[1,1,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([True, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0011","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c0221aba9a9ff93dffddaac059f8e722019335516492a6c066997c12d9d6a59","family_id":"qf-density13-connectives-and-or-table","seed":202610135011,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [False, False, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0012","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f1823970689a1130c492969f44de8652282aa0e73298a81e03915798155f381","family_id":"qf-density13-connectives-and-or-table","seed":202610135012,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [True, False, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [True, False, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0013","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d73620b83d087df020996dbdc6457b04e021f24dae12a15a0c99ff21a9dafcbe","family_id":"qf-density13-connectives-and-or-table","seed":202610135013,"semantic_template":"qf-density13-connectives-and-or-table/[[1,0,0,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([True, False, False, False, False, False, False, False], [True, False, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, False, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0014","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc2fbec10d327487987e7c0ba0b01ae6aa173503e4dd4ace4f1ecb83e723c52f","family_id":"qf-density13-connectives-and-or-table","seed":202610135014,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [False, True, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, True, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0015","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf63b5b2e5cf9e8376f8a75af1142c220430f28dbb9799150ad7e89cfc95f8d1","family_id":"qf-density13-connectives-and-or-table","seed":202610135015,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0016","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dac4224bd1989de0af1a7d5e758cf8f7058881a97b777244ba7f26fa85e8a38c","family_id":"qf-density13-connectives-and-or-table","seed":202610135016,"semantic_template":"qf-density13-connectives-and-or-table/[[1,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([True, False, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0017","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec1c77d77730fefb62c6c086c2cb77b1b369cbc375d9650d834b4bbb1b7108ba","family_id":"qf-density13-connectives-and-or-table","seed":202610135017,"semantic_template":"qf-density13-connectives-and-or-table/[[0,1,0,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, True, False, False, False, False, False, False], [False, True, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [False, True, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0018","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"350bbdf17849e3b1ad49eda4c724acb36f4668aed6b6d41662c205b436622050","family_id":"qf-density13-connectives-and-or-table","seed":202610135018,"semantic_template":"qf-density13-connectives-and-or-table/[[0,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0019","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"de191ea937aa648302d4d6cc623b19c22b8dd104de6573a99eca07500ef04ba7","family_id":"qf-density13-connectives-and-or-table","seed":202610135019,"semantic_template":"qf-density13-connectives-and-or-table/[[1,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([True, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0020","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78c301d0982a6b8d33e1f4b61e7110d2d209b8dc8446d667d99686f3e1bd3ec8","family_id":"qf-density13-connectives-and-or-table","seed":202610135020,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0021","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"302895e3e8f138ce50c1ddf4b787690ddd55327bf3d6655725faf5364f010b7d","family_id":"qf-density13-connectives-and-or-table","seed":202610135021,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0022","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ce57a9abea8c44f4db73918362195b92a8a46c9770950db1cd1038dab3d3115","family_id":"qf-density13-connectives-and-or-table","seed":202610135022,"semantic_template":"qf-density13-connectives-and-or-table/[[1,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([True, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0023","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd774556592e20dddfaa642e55a1082e3e417b39a8106bd821aacebd88355dc2","family_id":"qf-density13-connectives-and-or-table","seed":202610135023,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,1,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0024","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"91ffef5cfb040a738f641fc945bc42faf3bff537fab5ea3a32c883f81c82a3d0","family_id":"qf-density13-connectives-and-or-table","seed":202610135024,"semantic_template":"qf-density13-connectives-and-or-table/[[0,0,1,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([False, False, True, False, False, False, False, False], [True, True, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [True, True, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0025","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f5a13b9b7b92cd16b9abc066c488e8ae5f3ce95ebf9233b6351478b1975974b2","family_id":"qf-density13-connectives-and-or-table","seed":202610135025,"semantic_template":"qf-density13-connectives-and-or-table/[[1,0,1,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"},"fields":{"title":"Conjunction and Inclusive Disjunction Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).","answer":{"kind":"expression","value":"([True, False, True, False, False, False, False, False], [True, True, True, False, False, False, False, False])","explanation":"Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [True, True, True, False, False, False, False, False])."},"skills":["Conjunction and Inclusive Disjunction Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0026","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e3ebeb05ad7dc115912fd3e527d30effeb40fd68c7651d5b3d51e0fdcdd50380","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135026,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0027","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"502d2fc29a32ad8e607592f0fb2d8ec705ff1f9fb83a90be25135582c1c139e9","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135027,"semantic_template":"qf-density13-connectives-implication-biconditional/[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0028","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc5dd77dc358e00a7441da20ae9b80f96f591c2fce0826c2275c4ea399ffe756","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135028,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[1, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0029","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"311669d6e05cf2ef84b1549788b426cd8e8f1f607a2e53913342db64b69ff05e","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135029,"semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([False, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0030","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2fa42f84571daaf03922bb9721a92c24bc3b041bc743f36a41dedc2fd5ca50e6","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135030,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[1,0,1,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[0, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [True, False, True, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, False, True, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0031","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"40761fb24aeb3f63b8274822caf1a5f69f5e991ec93b0caf5e5b0d351b4ca8d5","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135031,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[0,0,1,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[1, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0032","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc7bd5ad2ae59d318448fdefd14ba3c097d15d8210cfb0b6a8db999fa63f00b3","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135032,"semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,1,1,1,1,1,1],[0,0,1,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 1], B=[0, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([False, True, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0033","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e30780980c0208eeb369ef02e2226b910d9aaeb4c3b33518e9f2e0351697b3d1","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135033,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,0,1,1,1,1,1,1],[1,0,1,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, False, True, True, True, True, True, True], [True, False, True, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [True, False, True, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0034","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87d30a53f0ba37843ae7b0a6d64d754f884444f3e976541d6988351aaeceb968","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135034,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,0,1,1,1,1,1,1],[0,0,1,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 1], B=[1, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0035","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"675aae2ff983d19b714b1a39ac43e66e7fe0db9ed486bc50c01b848c1d88861b","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135035,"semantic_template":"qf-density13-connectives-implication-biconditional/[[0,0,1,1,1,1,1,1],[0,0,1,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([False, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0036","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45c20e5516f7da75c34ed0478d5493dda8e2aba038a2c7d5477383bb5d28c77b","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135036,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[1,1,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[0, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [True, True, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, True, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0037","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d599714fa95ae43033155d48fd4ce901a89419c665faafa41e2b2171f206b6be","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135037,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[0,1,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[1, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [False, True, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, True, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0038","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"621c84d85513407d4ea0471e7d0383690391e8b03a7f97aa9507aeb1282cb7f9","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135038,"semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,1,1,1,1,1,1],[0,1,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 1], B=[0, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([False, True, True, True, True, True, True, True], [False, True, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, True, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0039","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9f8dd7a1c0d843f7a659255522ded12ca84298200dc1975aafa119514106c29","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135039,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[1,0,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[0, 1, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [True, False, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, False, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0040","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c54838b15d661a6db482cb3f55df4ff64496388426d3d1e86d114c6e279e111","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135040,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[1, 1, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0041","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"afee3031cea832c40e74189fbf86df4d7f8fd80b8a78a391eb17a8fc3ca5802a","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135041,"semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,1,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 1], B=[0, 1, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([False, True, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0042","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1925ccd9d0c1e8181db7ab0f4faed4c3446865e54975088b27c092cc52315886","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135042,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,0,1,1,1,1,1,1],[1,0,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 1], B=[0, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, False, True, True, True, True, True, True], [True, False, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [True, False, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0043","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20613bcecf517e2666458d034b478d0b1031a216fd566cb4a401e899aca4afe2","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135043,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,0,1,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 1], B=[1, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, False, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0044","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6452541bc9c449ec97def660bbe8eef52ee83ee64b6c8be764f66aac4250717b","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135044,"semantic_template":"qf-density13-connectives-implication-biconditional/[[0,0,1,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 1], B=[0, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([False, False, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0045","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ea3a23fa92f6e3cf98b2c755e615154b2ec5f04065a87293e6c555499262c992","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135045,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,0,1,1,1,1,1],[1,1,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, False, True, True, True, True, True], [True, True, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [True, True, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0046","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2e56a646f9f02a32fd5272464099ab996ec1ced514d6b32ab26bbea381eeea10","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135046,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,0,1,1,1,1,1],[0,1,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 1], B=[1, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0047","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0de0e9943c3c4af1d341208fc9bfc146dcfc5808c70557fb121a1d1bc044b796","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135047,"semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,0,1,1,1,1,1],[0,1,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([False, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0048","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2a4c63cf349a7d8c7298a5c227f24ca634d1e085d00ffa38dc895bb70905f291","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135048,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,0,1,1,1,1,1],[1,0,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 1], B=[0, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, False, True, True, True, True, True], [True, False, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [True, False, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0049","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1183dd54f28c53b926f3977cc8003e674e290a6a53435c1a76c57c6a68d544d4","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135049,"semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,0,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 1], B=[1, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([True, True, False, True, True, True, True, True], [False, False, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [False, False, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0050","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e5e181a854dca7cd12432d6e37bca2e05c63ef3882142beb5dd387fb1775c88","family_id":"qf-density13-connectives-implication-biconditional","seed":202610135050,"semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,0,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"},"fields":{"title":"Material Implication and Biconditional Tables","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 1], B=[0, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).","answer":{"kind":"expression","value":"([False, True, False, True, True, True, True, True], [False, False, False, True, True, True, True, True])","explanation":"Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, True, True, True, True, True], [False, False, False, True, True, True, True, True])."},"skills":["Material Implication and Biconditional Tables"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0051","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53c71eefd9e87ce6c541ae859f18605d65a721e2c11160d3a4594d3f4e99b4f4","family_id":"qf-density13-connectives-demorgan-table","seed":202610135051,"semantic_template":"qf-density13-connectives-demorgan-table/[1,1,1,1,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0052","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f798e583bb35fc95d4f705f589a0083f3fff6b96080358b765673f36db5c3886","family_id":"qf-density13-connectives-demorgan-table","seed":202610135052,"semantic_template":"qf-density13-connectives-demorgan-table/[0,0,0,0,0,0,0,0]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 1, 1, 1, 1, 1]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0053","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"512d035aa2c7c6cbd5f66241ed82d789c6373a8752430844e69a0f14ada498ec","family_id":"qf-density13-connectives-demorgan-table","seed":202610135053,"semantic_template":"qf-density13-connectives-demorgan-table/[0,1,1,1,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0054","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc120cdb433c8f3114ff37191df5c349c6459e8893e891798aaaf662cf2637fc","family_id":"qf-density13-connectives-demorgan-table","seed":202610135054,"semantic_template":"qf-density13-connectives-demorgan-table/[1,0,1,1,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, False, True, True, True, True, True, True], [True, False, True, True, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [True, False, True, True, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0055","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"86b51f8de811bf7649b731013b9576fd5f9a01064e9228281a716a3344deb732","family_id":"qf-density13-connectives-demorgan-table","seed":202610135055,"semantic_template":"qf-density13-connectives-demorgan-table/[0,0,1,1,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0056","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab2a934b5a32d47d7c45966d88cbae805fcf295d836bfd2218a0b1fdcc0abf4d","family_id":"qf-density13-connectives-demorgan-table","seed":202610135056,"semantic_template":"qf-density13-connectives-demorgan-table/[1,1,0,1,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, True, False, True, True, True, True, True], [True, True, False, True, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [True, True, False, True, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0057","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"49c57910243eebabf0d128855ac60712de9ea9293846259fd9837f32138e156a","family_id":"qf-density13-connectives-demorgan-table","seed":202610135057,"semantic_template":"qf-density13-connectives-demorgan-table/[0,1,0,1,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0058","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"563007affd746ba1aa28054ce6d88cc0800172abb7629d1728be0eac03bad0ee","family_id":"qf-density13-connectives-demorgan-table","seed":202610135058,"semantic_template":"qf-density13-connectives-demorgan-table/[1,0,0,1,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 1, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, False, False, True, True, True, True, True], [True, False, False, True, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, True, True, True, True, True], [True, False, False, True, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0059","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7497e272cbc04e3bdb0eaa20096fc4520e3235b4013ad2c9138dc7095b28625e","family_id":"qf-density13-connectives-demorgan-table","seed":202610135059,"semantic_template":"qf-density13-connectives-demorgan-table/[0,0,0,1,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, False, False, True, True, True, True, True], [False, False, False, True, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, True, True, True, True, True], [False, False, False, True, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0060","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0ebe911834ec39bc3d4490be98e41e2573283d29f952c3934e1a882ce06f3ef","family_id":"qf-density13-connectives-demorgan-table","seed":202610135060,"semantic_template":"qf-density13-connectives-demorgan-table/[1,1,1,0,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 0, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, True, True, False, True, True, True, True], [True, True, True, False, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, True, True, True, True], [True, True, True, False, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0061","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"95da7e401e1588c07298a8a4617cb6ec2b02874bf151268f5090fe6ada715f2c","family_id":"qf-density13-connectives-demorgan-table","seed":202610135061,"semantic_template":"qf-density13-connectives-demorgan-table/[0,1,1,0,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 0, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, True, True, False, True, True, True, True], [False, True, True, False, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, False, True, True, True, True], [False, True, True, False, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0062","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7beaa7757298e073dc1b9e71aa7dcf94b41ca875f996906ec3cfe919531965b3","family_id":"qf-density13-connectives-demorgan-table","seed":202610135062,"semantic_template":"qf-density13-connectives-demorgan-table/[1,0,1,0,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 0, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, False, True, False, True, True, True, True], [True, False, True, False, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, True, True, True, True], [True, False, True, False, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0063","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7a4033983a56bbaec00ff3a479617322885bdf58530de70ce5a23f5734d3a6aa","family_id":"qf-density13-connectives-demorgan-table","seed":202610135063,"semantic_template":"qf-density13-connectives-demorgan-table/[0,0,1,0,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 0, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, False, True, False, True, True, True, True], [False, False, True, False, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, True, True, True, True], [False, False, True, False, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0064","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c390a1675653fac1474a049577c3ac99450ed6328c0b27d5b9a85160523c60a","family_id":"qf-density13-connectives-demorgan-table","seed":202610135064,"semantic_template":"qf-density13-connectives-demorgan-table/[1,1,0,0,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 1, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, True, False, False, True, True, True, True], [True, True, False, False, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, True, True, True, True], [True, True, False, False, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0065","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c258e10f6ac2abe69fe0393063481d25854f9365796234af6532dc9856bfeae","family_id":"qf-density13-connectives-demorgan-table","seed":202610135065,"semantic_template":"qf-density13-connectives-demorgan-table/[0,1,0,0,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 1, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, True, False, False, True, True, True, True], [False, True, False, False, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, True, True, True, True], [False, True, False, False, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0066","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4685cd15fd2aa6a15f132bac2c731f3d94499773411b84f0bbc7449ac81fb746","family_id":"qf-density13-connectives-demorgan-table","seed":202610135066,"semantic_template":"qf-density13-connectives-demorgan-table/[1,0,0,0,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 1, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, False, False, False, True, True, True, True], [True, False, False, False, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, True, True, True, True], [True, False, False, False, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0067","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"60d233c7592b3e5d161e7ab57452757baf7261eb3a47f3aef82fee61cd987a49","family_id":"qf-density13-connectives-demorgan-table","seed":202610135067,"semantic_template":"qf-density13-connectives-demorgan-table/[0,0,0,0,1,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, False, False, False, True, True, True, True], [False, False, False, False, True, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, True, True, True, True], [False, False, False, False, True, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0068","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fae6e0ca9869bcd2a69e8413387a20553ab33d6ffd6d7aad8b707212a0365e48","family_id":"qf-density13-connectives-demorgan-table","seed":202610135068,"semantic_template":"qf-density13-connectives-demorgan-table/[1,1,1,1,0,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 0, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, True, True, True, False, True, True, True], [True, True, True, True, False, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, False, True, True, True], [True, True, True, True, False, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0069","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b6bf00665b8915a8376b8e1a2b962c4ea4cdb73be936421285ba6764070b29e6","family_id":"qf-density13-connectives-demorgan-table","seed":202610135069,"semantic_template":"qf-density13-connectives-demorgan-table/[0,1,1,1,0,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 0, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, True, True, True, False, True, True, True], [False, True, True, True, False, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, False, True, True, True], [False, True, True, True, False, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0070","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0d3c0e914345ee4e94e277911bc1c5fad97ee3d43e026c3c5aeb29a4d24bd028","family_id":"qf-density13-connectives-demorgan-table","seed":202610135070,"semantic_template":"qf-density13-connectives-demorgan-table/[1,0,1,1,0,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 0, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, False, True, True, False, True, True, True], [True, False, True, True, False, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, False, True, True, True], [True, False, True, True, False, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0071","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"37d222c27aeaca4e3113f2060d563a372590a5b0552877a4fbac643b14ee97b8","family_id":"qf-density13-connectives-demorgan-table","seed":202610135071,"semantic_template":"qf-density13-connectives-demorgan-table/[0,0,1,1,0,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 0, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, False, True, True, False, True, True, True], [False, False, True, True, False, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, True, False, True, True, True], [False, False, True, True, False, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0072","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2449e367c4a0068cfa8ca16b457d39d29e364bbd59802d5079d1b8cae25460e9","family_id":"qf-density13-connectives-demorgan-table","seed":202610135072,"semantic_template":"qf-density13-connectives-demorgan-table/[1,1,0,1,0,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 1, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, True, False, True, False, True, True, True], [True, True, False, True, False, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, False, True, True, True], [True, True, False, True, False, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0073","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"32741e9d5b11977b98601b88c10c8a13f7c63438579f832800263d8c37c4ce61","family_id":"qf-density13-connectives-demorgan-table","seed":202610135073,"semantic_template":"qf-density13-connectives-demorgan-table/[0,1,0,1,0,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 1, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, True, False, True, False, True, True, True], [False, True, False, True, False, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, True, False, True, True, True], [False, True, False, True, False, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0074","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"02eb335555e4aa65c765821f864a88b351537692a292d0478866633c96dc1609","family_id":"qf-density13-connectives-demorgan-table","seed":202610135074,"semantic_template":"qf-density13-connectives-demorgan-table/[1,0,0,1,0,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 1, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([True, False, False, True, False, True, True, True], [True, False, False, True, False, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, True, False, True, True, True], [True, False, False, True, False, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0075","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a730c27e7d48a51a26336104eee0de7ed70097d3b0b8eee0dc6504ef44e401dd","family_id":"qf-density13-connectives-demorgan-table","seed":202610135075,"semantic_template":"qf-density13-connectives-demorgan-table/[0,0,0,1,0,1,1,1]"},"fields":{"title":"Two Complete De Morgan Computations","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.","answer":{"kind":"expression","value":"([False, False, False, True, False, True, True, True], [False, False, False, True, False, True, True, True])","explanation":"One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, True, False, True, True, True], [False, False, False, True, False, True, True, True])."},"skills":["Two Complete De Morgan Computations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0076","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"398e4eeac2684658115012a2a886a7842bbc34e8880a04b7da6c27f8c5c0b2e1","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135076,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0077","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64998045c6d70b883fad4036e9067f8f4252f2adc1e9c136b0e66e9420af9288","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135077,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,1,1,1,1,1],[0,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 1, 1, 1, 1, 1]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, True, True, True, True, True, True], [False, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0078","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a08d7d93e08c0f423d27bfa77018e9a968a4d05b88b924efa7c46f531682a74b","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135078,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0079","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fda98dfd548400b6e57cbd644e4188d632fa6d23b84357db83f056fb5952ac89","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135079,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0080","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c675afe8858eccaf1e35013f8204f4abf98cfbeecffcb5804250d906584177b2","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135080,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([False, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0081","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1343df37707cef8f1131bff3068296fcac10b49332d98e551cc46ffcad99047","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135081,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0082","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"85c87756ec97de04ed72321cbd85b6eaf2a491c103d3645fa3c7adb787020deb","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135082,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0083","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a2e2268ff8d626073019cb734f7b6857465ce2722372163fb71d71578185ee97","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135083,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([False, True, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0084","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a46c4ce7352b699ccef7d224cf2ad0b5b3a3e6777957163af418bb48fbec0696","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135084,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0085","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3319bcbf9fe02e88453e252d593ebf901aca5816cc7cb1b9270aa7348648a8da","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135085,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0086","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a83af4a9a4b4e032cae68054f47d9c7dcffc5ef45f7db97aca86f00c9e755654","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135086,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([False, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0087","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd05685053d868624f8a4024561731082921259fa1292cbaed06ba161e5c2a91","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135087,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0088","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b66381ca0d5aac852ac31243d5d83403317fc3a9f12cce0035644ff12c7d5ff","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135088,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0089","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a660cfe56f9681a20eabb4556a4247564d6b4bfb9e09626a0ddef13d1e6846bd","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135089,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,1,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([False, True, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0090","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23cb172ef4bf7940490d5feac02b3ac3df4d07850337d407edf1cb694ffcfdb1","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135090,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, True, False, False, False, False, False], [True, True, True, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [True, True, True, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0091","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae1a51bd29fe7ba5be06616a20c62795e00fbafcfbf42007b770bc92637e4165","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135091,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0092","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf0a74ac3ab1b90ff0481a103ced370136d83abf43dd87708e636febd79e3c79","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135092,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([False, True, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0093","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"600510d721d7f6dbe41b0039f4a5af1263662b75284299b0494679f35d76cfa7","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135093,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0094","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04c6dbb1d84540627bbd2954be776e3330d9505c3d0bacafad55294ebae86b19","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135094,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0095","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d6111fcb8d9b560b126798ddbd5fef9ee12ee525b642f3e2caa804f3439b2971","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135095,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([False, False, True, False, False, False, False, False], [False, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [False, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0096","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4e496c647149aa719d7726de8e60fd96ccac8496736e1a473952a7064192322","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135096,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, False, True, False, False, False, False, False], [True, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [True, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0097","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9a38bae1f338ad00f0eef435e2a1d3097b24dd1a0a072fc1a0a04acd6548ed6e","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135097,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, False, True, False, False, False, False, False], [False, False, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [False, False, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0098","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1cef9f432ee5c063616e9355745e0f5b9455ed2f69f0f567fc141ef7e7022949","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135098,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([False, True, True, False, False, False, False, False], [False, True, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, False, False, False, False, False], [False, True, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0099","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a1e2f5e892570470d17673c7b6d9123a7f4b0829f140a73046b82b4244123e75","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135099,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, True, False, False, False, False, False], [True, True, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [True, True, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261009-advance-20261013-r05-logical-connectives-0100","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee39daf609b74ac1bc09617c6ac1680c62d25eb59aebb6d27e7c2c69d6e3f2f2","family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135100,"semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"},"fields":{"title":"Inclusive Disjunction versus Exactly-One Truth","stem":"Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.","answer":{"kind":"expression","value":"([True, True, True, False, False, False, False, False], [False, True, False, False, False, False, False, False])","explanation":"Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [False, True, False, False, False, False, False, False])."},"skills":["Inclusive Disjunction versus Exactly-One Truth"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}