{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261010-r02-set-operations-0001","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa619d978530132b084d7bc50f0152688f8d7972c72c391fad23005bfb6a6ad6","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102001,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,0],0]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[] and B=[]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(0, 0)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (0, 0)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0002","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"02d6d971d91495e35e8b33d1056eaa90b9b56c944bfc754db1f6b84336732fe6","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102002,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,0],1]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0] and B=[0]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(1, 1)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (1, 1)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0003","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"37d6ba80272dc3ef58ac602cedb2e0feb467f3c14dbc1145613e08893c100354","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102003,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,1],0]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[] and B=[100]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(1, 0)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (1, 0)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0004","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"86019aa36eb24b70d4bdbd19df9d7eccf1ba4bc2e963a7d89e1ebbedd495425a","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102004,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,0],2]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1] and B=[0, 1]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(2, 2)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (2, 2)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0005","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc5b515202e2bf8fd7c8bcd193fee4f4fa81a2de966ed2577122d2aa4b57a0de","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102005,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,1],1]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0] and B=[0, 100]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(2, 1)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (2, 1)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0006","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c32c8dca8dc10fd598eeb5c620ccf7e12ef16d2039d1bfc2f85823ba6bdf81ab","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102006,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,2],0]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[] and B=[100, 101]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(2, 0)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (2, 0)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0007","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"24eedbea86a1552a2ccd7b5794bbd9812b329beecd7a1df985ebd36e9d540016","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102007,"semantic_template":"qf-density10-set-union-intersection-sizes/[[1,1],0]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[-1] and B=[100]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(2, 0)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (2, 0)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0008","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e62a6fdeb079d7b04f77bb3ed9b406a44bf89062b49b1533e8c694926a6ef495","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102008,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,0],3]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1, 2] and B=[0, 1, 2]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(3, 3)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (3, 3)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0009","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6c2125826c8641013fce8f0c6e43d341e339d217a68709f1c396c1b03cf9a4c6","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102009,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,1],2]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1] and B=[0, 1, 100]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(3, 2)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (3, 2)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0010","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1bd9e4d6c6012a0240858e510f8320c20e6c40116665a23ceded25813873514a","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102010,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,2],1]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0] and B=[0, 100, 101]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(3, 1)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (3, 1)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0011","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2fe0844e660b892cba892b55ab1284d4d225976f2a5e7956baa2ea3563df2020","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102011,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,3],0]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[] and B=[100, 101, 102]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(3, 0)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (3, 0)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0012","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4cd50892425142a21977782fb622770c57b33638eaee24e4626d6ae29bdef528","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102012,"semantic_template":"qf-density10-set-union-intersection-sizes/[[1,1],1]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, -1] and B=[0, 100]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(3, 1)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (3, 1)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0013","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"968340a2496b0214a025fa9ef8078dea3cd4d3f10655f68eac0e95cec535e206","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102013,"semantic_template":"qf-density10-set-union-intersection-sizes/[[1,2],0]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[-1] and B=[100, 101]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(3, 0)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (3, 0)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0014","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"947c10bbcee1c67bc2b557cabbaa0a1ddb269653f256ca3ed79e4807a1dd60b5","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102014,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,0],4]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1, 2, 3] and B=[0, 1, 2, 3]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(4, 4)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (4, 4)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0015","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"afb1f8060e9b1fba403685f44b478422e58416807ca4106295ce1e17d1921abd","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102015,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,1],3]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1, 2] and B=[0, 1, 2, 100]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(4, 3)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (4, 3)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0016","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"25b1c1f0c7695b736f5d4c6692d737844b4ba43093be37d3a3afb6ec11bda2b1","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102016,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,2],2]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1] and B=[0, 1, 100, 101]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(4, 2)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (4, 2)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0017","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7689ce41fe1ad701d0fbc3f1c86dba1701818b109017be1c357d0de9a437caba","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102017,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,3],1]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0] and B=[0, 100, 101, 102]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(4, 1)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (4, 1)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0018","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eb123332ef4bb82bff1c400673d0db2dcc917003fa071ad98ecb82f61feef7eb","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102018,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,4],0]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[] and B=[100, 101, 102, 103]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(4, 0)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (4, 0)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0019","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04c7b20f2ed7305168a70a385f5a41e6a0e37e0c36c6dcca549791f6803288ee","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102019,"semantic_template":"qf-density10-set-union-intersection-sizes/[[1,1],2]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1, -1] and B=[0, 1, 100]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(4, 2)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (4, 2)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0020","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3dd093b9d1c80dc22b4be117fc114974606aa78f7c7f58f2b37939e4113d7071","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102020,"semantic_template":"qf-density10-set-union-intersection-sizes/[[1,2],1]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, -1] and B=[0, 100, 101]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(4, 1)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (4, 1)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0021","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"50a29b207d2eeed810b85f055b1fa4d65546f9d1aee34eeacb9be8b88215d2a5","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102021,"semantic_template":"qf-density10-set-union-intersection-sizes/[[1,3],0]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[-1] and B=[100, 101, 102]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(4, 0)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (4, 0)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0022","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fb6bc93ad3dfcb9cb47e3233a98f413057f175845a0c7eeedb111373856add92","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102022,"semantic_template":"qf-density10-set-union-intersection-sizes/[[2,2],0]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[-2, -1] and B=[100, 101]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(4, 0)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (4, 0)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0023","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"08c3992ba3114df102cc844522402f541e5815f3192dd1c87188fac5a636f64b","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102023,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,0],5]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1, 2, 3, 4] and B=[0, 1, 2, 3, 4]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(5, 5)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (5, 5)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0024","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f310bef5355856ca66150018a6e583be07339bc20c047ab7ce2fd319ecca0695","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102024,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,1],4]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1, 2, 3] and B=[0, 1, 2, 3, 100]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(5, 4)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (5, 4)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0025","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"be493093a7f939bd360b0227117e8a21dd219c638db11974be2943c677e3baef","family_id":"qf-density10-set-union-intersection-sizes","seed":202610102025,"semantic_template":"qf-density10-set-union-intersection-sizes/[[0,2],3]"},"fields":{"title":"Union and Intersection Cardinalities","stem":"Finite integer sets A=[0, 1, 2] and B=[0, 1, 2, 100, 101]; repeated elements count once. Give (|A∪B|, |A∩B|).","answer":{"kind":"expression","value":"(5, 3)","explanation":"Count membership in the two sets; common elements enter the union once, and the empty set has size zero. The exact result, retaining the requested order, is (5, 3)."},"skills":["Union and Intersection Cardinalities"],"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-20261008-advance-20261010-r02-set-operations-0026","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2970c4626ffcbe3db6157f3fccf632dbd979d5df2d90626f3bff545bd7d5ca26","family_id":"qf-density10-set-symmetric-difference","seed":202610102026,"semantic_template":"qf-density10-set-symmetric-difference/[[],[]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[] and B=[]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is []."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0027","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ed364c4fe25c01c636745fe557b7ceade3e93f6c8bc84884c04aed43c063da8e","family_id":"qf-density10-set-symmetric-difference","seed":202610102027,"semantic_template":"qf-density10-set-symmetric-difference/[[0,1],[0,1]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[0, 1] and B=[0, 1]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is []."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0028","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9b25ad1664f39392067181de6638e6da2585e955bbd3d4d35a343133af832d5","family_id":"qf-density10-set-symmetric-difference","seed":202610102028,"semantic_template":"qf-density10-set-symmetric-difference/[[-2,2],[]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[] and B=[-2, 2]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-2, 2]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-2, 2]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0029","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1e0c404972a292137b958e5ab4d4cdf315a592d63926ec16a7994c2d7bd0b964","family_id":"qf-density10-set-symmetric-difference","seed":202610102029,"semantic_template":"qf-density10-set-symmetric-difference/[[-3,0,3],[0,4]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-3, 0, 3] and B=[0, 4]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-3, 3, 4]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-3, 3, 4]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0030","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"09d90a9472eac4c62112da331d22a23762705f5cbc2a7c5f73925f9857698e69","family_id":"qf-density10-set-symmetric-difference","seed":202610102030,"semantic_template":"qf-density10-set-symmetric-difference/[[-4,0,4],[0,5]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-4, 0, 4] and B=[0, 5]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-4, 4, 5]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-4, 4, 5]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0031","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f2665920e8fd16550a69610d24ededdabeaf9a9026f78ebb65bb3584f94690ff","family_id":"qf-density10-set-symmetric-difference","seed":202610102031,"semantic_template":"qf-density10-set-symmetric-difference/[[-5,0,5],[0,6]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-5, 0, 5] and B=[0, 6]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-5, 5, 6]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-5, 5, 6]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0032","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca0a1518956a76f9a2ca4c6d49d60013e24d3588a56aa536cca51e5d5599385c","family_id":"qf-density10-set-symmetric-difference","seed":202610102032,"semantic_template":"qf-density10-set-symmetric-difference/[[-6,0,6],[0,7]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-6, 0, 6] and B=[0, 7]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-6, 6, 7]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-6, 6, 7]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0033","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f711175bf10d466caff0f9dd93e1a51ae27e7763b30aad974c4ddba2ddea862a","family_id":"qf-density10-set-symmetric-difference","seed":202610102033,"semantic_template":"qf-density10-set-symmetric-difference/[[-7,0,7],[0,8]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-7, 0, 7] and B=[0, 8]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-7, 7, 8]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-7, 7, 8]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0034","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d71f86b18abc67e154cf8f8d01e4fe72c9178b8e87ce0bb2337ec9ed185b068","family_id":"qf-density10-set-symmetric-difference","seed":202610102034,"semantic_template":"qf-density10-set-symmetric-difference/[[-8,0,8],[0,9]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-8, 0, 8] and B=[0, 9]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-8, 8, 9]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-8, 8, 9]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0035","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a60c2e5ca29deb9a3f06d97a110cf1a42396239d50e2f3d071c7fc4c92671d5","family_id":"qf-density10-set-symmetric-difference","seed":202610102035,"semantic_template":"qf-density10-set-symmetric-difference/[[-9,0,9],[0,10]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-9, 0, 9] and B=[0, 10]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-9, 9, 10]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-9, 9, 10]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0036","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3ec8c3d95153753c109600173430783cb9f3aa77378e07518c2cf089c1e14d95","family_id":"qf-density10-set-symmetric-difference","seed":202610102036,"semantic_template":"qf-density10-set-symmetric-difference/[[-10,0,10],[0,11]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-10, 0, 10] and B=[0, 11]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-10, 10, 11]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-10, 10, 11]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0037","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6a0072921c207b9fc4946b19af9116ab1c9ee3e68586d648421f3dddb3b56cf","family_id":"qf-density10-set-symmetric-difference","seed":202610102037,"semantic_template":"qf-density10-set-symmetric-difference/[[-11,0,11],[0,12]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-11, 0, 11] and B=[0, 12]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-11, 11, 12]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-11, 11, 12]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0038","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8de7f7e3fac37eda82674b3e4c64412d6f622c886352a7bc65e0e77dccc09944","family_id":"qf-density10-set-symmetric-difference","seed":202610102038,"semantic_template":"qf-density10-set-symmetric-difference/[[-12,0,12],[0,13]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-12, 0, 12] and B=[0, 13]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-12, 12, 13]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-12, 12, 13]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0039","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b7a0cc44bec676a25de5780b196fbba5624403e3dfd182c1a00cab8e10bb8c6","family_id":"qf-density10-set-symmetric-difference","seed":202610102039,"semantic_template":"qf-density10-set-symmetric-difference/[[-13,0,13],[0,14]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-13, 0, 13] and B=[0, 14]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-13, 13, 14]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-13, 13, 14]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0040","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd794d3084fd82cb650a66cf0a44beb24e243e1b6d5000bd4478ea74af69a50a","family_id":"qf-density10-set-symmetric-difference","seed":202610102040,"semantic_template":"qf-density10-set-symmetric-difference/[[-14,0,14],[0,15]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-14, 0, 14] and B=[0, 15]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-14, 14, 15]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-14, 14, 15]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0041","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c2a89f6f3fc88f35582aeea20278e1ead896f02aa9e8cac585179c306543b74f","family_id":"qf-density10-set-symmetric-difference","seed":202610102041,"semantic_template":"qf-density10-set-symmetric-difference/[[-15,0,15],[0,16]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-15, 0, 15] and B=[0, 16]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-15, 15, 16]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-15, 15, 16]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0042","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"caf7d4fdce40da47f9ecf241989a6800f877d192e6d0c075739926d2a4bfda75","family_id":"qf-density10-set-symmetric-difference","seed":202610102042,"semantic_template":"qf-density10-set-symmetric-difference/[[-16,0,16],[0,17]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-16, 0, 16] and B=[0, 17]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-16, 16, 17]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-16, 16, 17]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0043","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c763e8da7fc2be36ed69c3044be962a36dac01f78b4ef3df463ca5768c2f0401","family_id":"qf-density10-set-symmetric-difference","seed":202610102043,"semantic_template":"qf-density10-set-symmetric-difference/[[-17,0,17],[0,18]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-17, 0, 17] and B=[0, 18]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-17, 17, 18]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-17, 17, 18]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0044","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"11221c54059e81ac8d08b792f1d67282f2f86f37d7fcd9041056a45b09d320aa","family_id":"qf-density10-set-symmetric-difference","seed":202610102044,"semantic_template":"qf-density10-set-symmetric-difference/[[-18,0,18],[0,19]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-18, 0, 18] and B=[0, 19]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-18, 18, 19]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-18, 18, 19]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0045","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc837fdbd442c1b32096d73475e4426d19bc12a05a11f358440f09674b91dfca","family_id":"qf-density10-set-symmetric-difference","seed":202610102045,"semantic_template":"qf-density10-set-symmetric-difference/[[-19,0,19],[0,20]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-19, 0, 19] and B=[0, 20]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-19, 19, 20]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-19, 19, 20]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0046","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e2d340375fe4229f0d4ed1b6c51883ef46a94956ca3fb4942417228cb76be7f9","family_id":"qf-density10-set-symmetric-difference","seed":202610102046,"semantic_template":"qf-density10-set-symmetric-difference/[[-20,0,20],[0,21]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-20, 0, 20] and B=[0, 21]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-20, 20, 21]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-20, 20, 21]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0047","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c948dab923d84f2b4c92f71a8504dc07f7e21c59211f4e75343b4057e3ca8d0","family_id":"qf-density10-set-symmetric-difference","seed":202610102047,"semantic_template":"qf-density10-set-symmetric-difference/[[-21,0,21],[0,22]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-21, 0, 21] and B=[0, 22]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-21, 21, 22]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-21, 21, 22]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0048","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3086707625585d6c745e6f09229d33a1375b8f8ea9358fdf316b546de8ae0661","family_id":"qf-density10-set-symmetric-difference","seed":202610102048,"semantic_template":"qf-density10-set-symmetric-difference/[[-22,0,22],[0,23]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-22, 0, 22] and B=[0, 23]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-22, 22, 23]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-22, 22, 23]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0049","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df742acd7a1e0ac7dde484c173a34b3e4e6e17e51af5d5d85bc68ada6bec6e0e","family_id":"qf-density10-set-symmetric-difference","seed":202610102049,"semantic_template":"qf-density10-set-symmetric-difference/[[-23,0,23],[0,24]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-23, 0, 23] and B=[0, 24]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-23, 23, 24]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-23, 23, 24]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0050","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fda3376ad9eed83777262397af63efa9264fe0c1945528b4a10ab1bf60bc341c","family_id":"qf-density10-set-symmetric-difference","seed":202610102050,"semantic_template":"qf-density10-set-symmetric-difference/[[-24,0,24],[0,25]]"},"fields":{"title":"Sorted Symmetric Difference","stem":"Finite integer sets A=[-24, 0, 24] and B=[0, 25]; repeated elements count once. List (A\\B)∪(B\\A) in increasing order without repetition.","answer":{"kind":"expression","value":"[-24, 24, 25]","explanation":"Retain elements belonging to exactly one side; this is not the ordinary union. The exact result, retaining the requested order, is [-24, 24, 25]."},"skills":["Sorted Symmetric Difference"],"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-20261008-advance-20261010-r02-set-operations-0051","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c8bc58faad27a599be0eedd9722625e0379b125894baa7151dcf6ce79b4946d","family_id":"qf-density10-set-demorgan-sets","seed":202610102051,"semantic_template":"qf-density10-set-demorgan-sets/[[],[]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[] and B=[]; repeated elements count once. The explicit universe is U=[], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([], [])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([], [])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0052","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dcee3df599636af257f9b6bab077843badfbcf90b977f0411e8203f4010a9342","family_id":"qf-density10-set-demorgan-sets","seed":202610102052,"semantic_template":"qf-density10-set-demorgan-sets/[[-1,0,1],[-1,0,1]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[-1, 0] and B=[1]; repeated elements count once. The explicit universe is U=[-1, 0, 1], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([], [])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([], [])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0053","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7777a1447cfff69ad5584f03d4ecbe972f001cf9750f8025846be7afddc2a5bb","family_id":"qf-density10-set-demorgan-sets","seed":202610102053,"semantic_template":"qf-density10-set-demorgan-sets/[[-2,-1,0,1,2],[-1,0,2]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 2]; repeated elements count once. The explicit universe is U=[-2, -1, 0, 1, 2], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-2, 1], [-2, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-2, 1], [-2, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0054","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c93b1a241405b962ea6904faf11d790ac500bbd700f540d39fb88948ae2eb2c7","family_id":"qf-density10-set-demorgan-sets","seed":202610102054,"semantic_template":"qf-density10-set-demorgan-sets/[[-3,-1,0,1,3],[-1,0,3]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 3]; repeated elements count once. The explicit universe is U=[-3, -1, 0, 1, 3], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-3, 1], [-3, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-3, 1], [-3, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0055","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a95c7afa21a9524124071f18116b1bb49025353790eb50efdf3d29a7728edab","family_id":"qf-density10-set-demorgan-sets","seed":202610102055,"semantic_template":"qf-density10-set-demorgan-sets/[[-4,-1,0,1,4],[-1,0,4]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 4]; repeated elements count once. The explicit universe is U=[-4, -1, 0, 1, 4], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-4, 1], [-4, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-4, 1], [-4, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0056","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"37fdcf0cfb9f7d3b48e47d40d0f4c381e578e95cfea6a182e93f1c2e46e1742f","family_id":"qf-density10-set-demorgan-sets","seed":202610102056,"semantic_template":"qf-density10-set-demorgan-sets/[[-5,-1,0,1,5],[-1,0,5]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 5]; repeated elements count once. The explicit universe is U=[-5, -1, 0, 1, 5], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-5, 1], [-5, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-5, 1], [-5, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0057","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f8fdd556f85ce30ddc0c74be03c6a3f01f38ae3682e2b7e3f922078890a7a106","family_id":"qf-density10-set-demorgan-sets","seed":202610102057,"semantic_template":"qf-density10-set-demorgan-sets/[[-6,-1,0,1,6],[-1,0,6]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 6]; repeated elements count once. The explicit universe is U=[-6, -1, 0, 1, 6], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-6, 1], [-6, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-6, 1], [-6, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0058","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce2dee6e7254ac758f2df0a2d9279cb3e876aee13614a487b24da2c0699f3806","family_id":"qf-density10-set-demorgan-sets","seed":202610102058,"semantic_template":"qf-density10-set-demorgan-sets/[[-7,-1,0,1,7],[-1,0,7]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 7]; repeated elements count once. The explicit universe is U=[-7, -1, 0, 1, 7], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-7, 1], [-7, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-7, 1], [-7, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0059","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f5a992016d57bc2924e171dae8e7453a3be87cdaf27c9f856889e323aa460b2a","family_id":"qf-density10-set-demorgan-sets","seed":202610102059,"semantic_template":"qf-density10-set-demorgan-sets/[[-8,-1,0,1,8],[-1,0,8]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 8]; repeated elements count once. The explicit universe is U=[-8, -1, 0, 1, 8], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-8, 1], [-8, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-8, 1], [-8, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0060","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"86cc2de1294b2ecc5cf2f613fe2d7b7f00c5b9333f66759e50175b658294d8cd","family_id":"qf-density10-set-demorgan-sets","seed":202610102060,"semantic_template":"qf-density10-set-demorgan-sets/[[-9,-1,0,1,9],[-1,0,9]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 9]; repeated elements count once. The explicit universe is U=[-9, -1, 0, 1, 9], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-9, 1], [-9, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-9, 1], [-9, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0061","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a90d06c5157d526f00d072ddbfec7bebefd59ae71f1933834f8930a7c17fd4c7","family_id":"qf-density10-set-demorgan-sets","seed":202610102061,"semantic_template":"qf-density10-set-demorgan-sets/[[-10,-1,0,1,10],[-1,0,10]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 10]; repeated elements count once. The explicit universe is U=[-10, -1, 0, 1, 10], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-10, 1], [-10, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-10, 1], [-10, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0062","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f6cb5040780fe9720b43b823c97eb293c144338be97f9ca73f4ae23a09327c49","family_id":"qf-density10-set-demorgan-sets","seed":202610102062,"semantic_template":"qf-density10-set-demorgan-sets/[[-11,-1,0,1,11],[-1,0,11]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 11]; repeated elements count once. The explicit universe is U=[-11, -1, 0, 1, 11], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-11, 1], [-11, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-11, 1], [-11, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0063","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc5d90cb23f5f0702dc030109965b850f17c2114ced3cd1276236dd632ee1ce3","family_id":"qf-density10-set-demorgan-sets","seed":202610102063,"semantic_template":"qf-density10-set-demorgan-sets/[[-12,-1,0,1,12],[-1,0,12]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 12]; repeated elements count once. The explicit universe is U=[-12, -1, 0, 1, 12], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-12, 1], [-12, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-12, 1], [-12, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0064","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"06fb621125a0f45f85a39bbb730097cce41cacdc49165c3529037d6f5d131f34","family_id":"qf-density10-set-demorgan-sets","seed":202610102064,"semantic_template":"qf-density10-set-demorgan-sets/[[-13,-1,0,1,13],[-1,0,13]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 13]; repeated elements count once. The explicit universe is U=[-13, -1, 0, 1, 13], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-13, 1], [-13, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-13, 1], [-13, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0065","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce8f4dc1f6dc0cf0d2b75421dc75c57816f303cee788e699cc30cf75bb160193","family_id":"qf-density10-set-demorgan-sets","seed":202610102065,"semantic_template":"qf-density10-set-demorgan-sets/[[-14,-1,0,1,14],[-1,0,14]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 14]; repeated elements count once. The explicit universe is U=[-14, -1, 0, 1, 14], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-14, 1], [-14, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-14, 1], [-14, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0066","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1efaacc39d3a6d0bf3bd4d38d59380803ab227cc04d859053ea7229015b8e726","family_id":"qf-density10-set-demorgan-sets","seed":202610102066,"semantic_template":"qf-density10-set-demorgan-sets/[[-15,-1,0,1,15],[-1,0,15]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 15]; repeated elements count once. The explicit universe is U=[-15, -1, 0, 1, 15], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-15, 1], [-15, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-15, 1], [-15, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0067","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"38df1c33f65ca0eeb26f508d73ec539bfd8edcef8f8fbdc26a635d9a9bdeffec","family_id":"qf-density10-set-demorgan-sets","seed":202610102067,"semantic_template":"qf-density10-set-demorgan-sets/[[-16,-1,0,1,16],[-1,0,16]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 16]; repeated elements count once. The explicit universe is U=[-16, -1, 0, 1, 16], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-16, 1], [-16, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-16, 1], [-16, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0068","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4d00af5fd882502719979e0e5a9ff4f3270bc34adf8960288e53df1a9ebf1b43","family_id":"qf-density10-set-demorgan-sets","seed":202610102068,"semantic_template":"qf-density10-set-demorgan-sets/[[-17,-1,0,1,17],[-1,0,17]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 17]; repeated elements count once. The explicit universe is U=[-17, -1, 0, 1, 17], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-17, 1], [-17, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-17, 1], [-17, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0069","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6364b7c6b582d3332c91d56e24c13c33cf0e12bb8c5ea119ed88c183d1a1f6f5","family_id":"qf-density10-set-demorgan-sets","seed":202610102069,"semantic_template":"qf-density10-set-demorgan-sets/[[-18,-1,0,1,18],[-1,0,18]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 18]; repeated elements count once. The explicit universe is U=[-18, -1, 0, 1, 18], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-18, 1], [-18, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-18, 1], [-18, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0070","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"333e7d5be1d4ef3eb7bdbf6efa71192264bc110696a95e2018ae6e03aa8f0cd7","family_id":"qf-density10-set-demorgan-sets","seed":202610102070,"semantic_template":"qf-density10-set-demorgan-sets/[[-19,-1,0,1,19],[-1,0,19]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 19]; repeated elements count once. The explicit universe is U=[-19, -1, 0, 1, 19], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-19, 1], [-19, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-19, 1], [-19, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0071","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5cbc4863beb44c1b956d0b256fbddcfd16a417c0d61be4c147b8b1da38a3e996","family_id":"qf-density10-set-demorgan-sets","seed":202610102071,"semantic_template":"qf-density10-set-demorgan-sets/[[-20,-1,0,1,20],[-1,0,20]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 20]; repeated elements count once. The explicit universe is U=[-20, -1, 0, 1, 20], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-20, 1], [-20, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-20, 1], [-20, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0072","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da7b1ec684c161631e08cb8d2c116c5a6e71f3f1c5da2b0445fd325aff90acf4","family_id":"qf-density10-set-demorgan-sets","seed":202610102072,"semantic_template":"qf-density10-set-demorgan-sets/[[-21,-1,0,1,21],[-1,0,21]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 21]; repeated elements count once. The explicit universe is U=[-21, -1, 0, 1, 21], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-21, 1], [-21, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-21, 1], [-21, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0073","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a20e2118772857c1c984f78282e1f31a971ee43873638140788ea8476467fdd8","family_id":"qf-density10-set-demorgan-sets","seed":202610102073,"semantic_template":"qf-density10-set-demorgan-sets/[[-22,-1,0,1,22],[-1,0,22]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 22]; repeated elements count once. The explicit universe is U=[-22, -1, 0, 1, 22], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-22, 1], [-22, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-22, 1], [-22, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0074","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ea1ef83600bf662a8e8ddfcb7013c0ce68802c0095b4953fbf773e2607638094","family_id":"qf-density10-set-demorgan-sets","seed":202610102074,"semantic_template":"qf-density10-set-demorgan-sets/[[-23,-1,0,1,23],[-1,0,23]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 23]; repeated elements count once. The explicit universe is U=[-23, -1, 0, 1, 23], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-23, 1], [-23, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-23, 1], [-23, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0075","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f66fc19296282c1877bb610ad2acdb42d64704dc3ca4532c4148b9760e165e86","family_id":"qf-density10-set-demorgan-sets","seed":202610102075,"semantic_template":"qf-density10-set-demorgan-sets/[[-24,-1,0,1,24],[-1,0,24]]"},"fields":{"title":"Two Relative-Complement Computations","stem":"Finite integer sets A=[0] and B=[-1, 24]; repeated elements count once. The explicit universe is U=[-24, -1, 0, 1, 24], with A,B⊆U. Give (U\\(A∪B), (U\\A)∩(U\\B)), each sorted increasingly.","answer":{"kind":"expression","value":"([-24, 1], [-24, 1])","explanation":"Compute each route inside the declared universe; complements are not absolute. The exact result, retaining the requested order, is ([-24, 1], [-24, 1])."},"skills":["Two Relative-Complement 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-20261008-advance-20261010-r02-set-operations-0076","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"97c4fe21cf887e9cf1192fcdd56ddee647ecb29c9de3a276bbbcd5d2dee80ec7","family_id":"qf-density10-set-three-way-partition","seed":202610102076,"semantic_template":"qf-density10-set-three-way-partition/[[],[]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[] and B=[]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([], [], [])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([], [], [])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0077","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef7265f7f000fa95717526c982705186d2393b5003e653e25dd9e69769cce5b2","family_id":"qf-density10-set-three-way-partition","seed":202610102077,"semantic_template":"qf-density10-set-three-way-partition/[[-1,0],[0,1]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-1, 0] and B=[0, 1]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-1], [0], [1])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-1], [0], [1])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0078","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f6ddace30aff5a8e706aeec42edebb7ae24f10a6693b24e3e074147e88453276","family_id":"qf-density10-set-three-way-partition","seed":202610102078,"semantic_template":"qf-density10-set-three-way-partition/[[-2,0,2],[0,2,3]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-2, 0, 2] and B=[0, 2, 3]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-2], [0, 2], [3])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-2], [0, 2], [3])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0079","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"33bff60e4f03c488ea35277143ab758aa8dacec894fc9981140fb0cd650ee768","family_id":"qf-density10-set-three-way-partition","seed":202610102079,"semantic_template":"qf-density10-set-three-way-partition/[[-3,0,3],[0,3,4]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-3, 0, 3] and B=[0, 3, 4]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-3], [0, 3], [4])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-3], [0, 3], [4])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0080","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3ba7824b54f2f3418f6c84756ac8f2950ee521cd0c4ac1615483f0381976c183","family_id":"qf-density10-set-three-way-partition","seed":202610102080,"semantic_template":"qf-density10-set-three-way-partition/[[-4,0,4],[0,4,5]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-4, 0, 4] and B=[0, 4, 5]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-4], [0, 4], [5])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-4], [0, 4], [5])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0081","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a08ce45ed18dad2ec3d0dd632ec0f75e3d265fe3fb0a8596fa95970d0fd713c","family_id":"qf-density10-set-three-way-partition","seed":202610102081,"semantic_template":"qf-density10-set-three-way-partition/[[-5,0,5],[0,5,6]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-5, 0, 5] and B=[0, 5, 6]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-5], [0, 5], [6])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-5], [0, 5], [6])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0082","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac94f5547d127e720024d1c102ac655341be49d4dfcde685e8b6ea76a5c8b26b","family_id":"qf-density10-set-three-way-partition","seed":202610102082,"semantic_template":"qf-density10-set-three-way-partition/[[-6,0,6],[0,6,7]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-6, 0, 6] and B=[0, 6, 7]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-6], [0, 6], [7])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-6], [0, 6], [7])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0083","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac6964f9154a8e3fa0da64d2969d4054aaa5ac80f4ad4ebbb9c8a7195379a47a","family_id":"qf-density10-set-three-way-partition","seed":202610102083,"semantic_template":"qf-density10-set-three-way-partition/[[-7,0,7],[0,7,8]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-7, 0, 7] and B=[0, 7, 8]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-7], [0, 7], [8])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-7], [0, 7], [8])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0084","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5e7e0f0584857c0867d31794a3df8503f2be009c7f7f2baba43fdc6bf4a82b7a","family_id":"qf-density10-set-three-way-partition","seed":202610102084,"semantic_template":"qf-density10-set-three-way-partition/[[-8,0,8],[0,8,9]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-8, 0, 8] and B=[0, 8, 9]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-8], [0, 8], [9])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-8], [0, 8], [9])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0085","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a39c46cde38efa987db3c557c0a27b2e386d3d8b94f36b3b1e9f17a0919779b3","family_id":"qf-density10-set-three-way-partition","seed":202610102085,"semantic_template":"qf-density10-set-three-way-partition/[[-9,0,9],[0,9,10]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-9, 0, 9] and B=[0, 9, 10]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-9], [0, 9], [10])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-9], [0, 9], [10])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0086","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f4164656746e3c8121f065904ad028e02cc3c63907e72d56a1309f1c329987d","family_id":"qf-density10-set-three-way-partition","seed":202610102086,"semantic_template":"qf-density10-set-three-way-partition/[[-10,0,10],[0,10,11]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-10, 0, 10] and B=[0, 10, 11]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-10], [0, 10], [11])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-10], [0, 10], [11])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0087","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d71aa9ea3e14d47af3d6811e67424fb8e8cdc90adcbe44ec507e037d715c4ef8","family_id":"qf-density10-set-three-way-partition","seed":202610102087,"semantic_template":"qf-density10-set-three-way-partition/[[-11,0,11],[0,11,12]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-11, 0, 11] and B=[0, 11, 12]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-11], [0, 11], [12])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-11], [0, 11], [12])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0088","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31188ce53b1f622b694062b91a0148b24fc21dff992a8c94c57dbe0139b075db","family_id":"qf-density10-set-three-way-partition","seed":202610102088,"semantic_template":"qf-density10-set-three-way-partition/[[-12,0,12],[0,12,13]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-12, 0, 12] and B=[0, 12, 13]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-12], [0, 12], [13])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-12], [0, 12], [13])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0089","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e291e0fcbfeaffe5d59769c98617dcf8f526c43d2dcb83e4a6cd504a10daadc","family_id":"qf-density10-set-three-way-partition","seed":202610102089,"semantic_template":"qf-density10-set-three-way-partition/[[-13,0,13],[0,13,14]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-13, 0, 13] and B=[0, 13, 14]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-13], [0, 13], [14])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-13], [0, 13], [14])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0090","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2a0ac3ea04a9694e4194f38df28b0ce8b3ca88ca0a462a58196cded4ceb8c540","family_id":"qf-density10-set-three-way-partition","seed":202610102090,"semantic_template":"qf-density10-set-three-way-partition/[[-14,0,14],[0,14,15]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-14, 0, 14] and B=[0, 14, 15]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-14], [0, 14], [15])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-14], [0, 14], [15])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0091","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"be11fe26836790c45cf12c1710b700f58e01f28f093c1140d5417fdccd4b92b2","family_id":"qf-density10-set-three-way-partition","seed":202610102091,"semantic_template":"qf-density10-set-three-way-partition/[[-15,0,15],[0,15,16]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-15, 0, 15] and B=[0, 15, 16]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-15], [0, 15], [16])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-15], [0, 15], [16])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0092","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f34a43c4acd18c6c15d162c6146f26c05c74ba12e1dc7168fd6241e055eb46aa","family_id":"qf-density10-set-three-way-partition","seed":202610102092,"semantic_template":"qf-density10-set-three-way-partition/[[-16,0,16],[0,16,17]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-16, 0, 16] and B=[0, 16, 17]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-16], [0, 16], [17])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-16], [0, 16], [17])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0093","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b3cccdbf1ec454e1b77a68fe11d643d5501e3630455e075f72b2672ac493a6c7","family_id":"qf-density10-set-three-way-partition","seed":202610102093,"semantic_template":"qf-density10-set-three-way-partition/[[-17,0,17],[0,17,18]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-17, 0, 17] and B=[0, 17, 18]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-17], [0, 17], [18])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-17], [0, 17], [18])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0094","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"353eb9f8043fd8cff9abd911e7e6efab2b9af7f5d8c3788f68cb2561aee1d7fb","family_id":"qf-density10-set-three-way-partition","seed":202610102094,"semantic_template":"qf-density10-set-three-way-partition/[[-18,0,18],[0,18,19]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-18, 0, 18] and B=[0, 18, 19]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-18], [0, 18], [19])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-18], [0, 18], [19])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0095","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a0ef266c628a613aa9c5966e01a3b4de83139b90b10eda892979d0443568a7b7","family_id":"qf-density10-set-three-way-partition","seed":202610102095,"semantic_template":"qf-density10-set-three-way-partition/[[-19,0,19],[0,19,20]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-19, 0, 19] and B=[0, 19, 20]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-19], [0, 19], [20])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-19], [0, 19], [20])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0096","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c2cbdb694b63817b8c22f9c24b52eb69099f02a665f69fdd1e7cdce6157ce3a","family_id":"qf-density10-set-three-way-partition","seed":202610102096,"semantic_template":"qf-density10-set-three-way-partition/[[-20,0,20],[0,20,21]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-20, 0, 20] and B=[0, 20, 21]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-20], [0, 20], [21])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-20], [0, 20], [21])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0097","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"69e92d763e04831fd65a4c702443e36f218816a5031c1917b2575528cd287632","family_id":"qf-density10-set-three-way-partition","seed":202610102097,"semantic_template":"qf-density10-set-three-way-partition/[[-21,0,21],[0,21,22]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-21, 0, 21] and B=[0, 21, 22]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-21], [0, 21], [22])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-21], [0, 21], [22])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0098","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"facb84c5f82e5138e0295761c9cb26b425a6644cb58331b77ee41ef7c203a4c3","family_id":"qf-density10-set-three-way-partition","seed":202610102098,"semantic_template":"qf-density10-set-three-way-partition/[[-22,0,22],[0,22,23]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-22, 0, 22] and B=[0, 22, 23]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-22], [0, 22], [23])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-22], [0, 22], [23])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0099","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2e8f087f777efe384f1204f7074cfbc389b9fbb8071a1b25c6f9c1f34abccfba","family_id":"qf-density10-set-three-way-partition","seed":202610102099,"semantic_template":"qf-density10-set-three-way-partition/[[-23,0,23],[0,23,24]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-23, 0, 23] and B=[0, 23, 24]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-23], [0, 23], [24])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-23], [0, 23], [24])."},"skills":["Ordered Three-Part Set Partition"],"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-20261008-advance-20261010-r02-set-operations-0100","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9ab237337d9966e4f681e931ca7d0cdcae42cc5e6033be3629bd0df3b5018f0","family_id":"qf-density10-set-three-way-partition","seed":202610102100,"semantic_template":"qf-density10-set-three-way-partition/[[-24,0,24],[0,24,25]]"},"fields":{"title":"Ordered Three-Part Set Partition","stem":"Finite integer sets A=[-24, 0, 24] and B=[0, 24, 25]; repeated elements count once. Give (A\\B, A∩B, B\\A), each sorted increasingly, retaining empty parts.","answer":{"kind":"expression","value":"([-24], [0, 24], [25])","explanation":"Partition by left-only, common, and right-only membership without exchanging the two sides. The exact result, retaining the requested order, is ([-24], [0, 24], [25])."},"skills":["Ordered Three-Part Set Partition"],"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."}}