{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0001","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P1 與 Q1 的真值分別為 真、真。P1 與 Q1 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P1 與 Q1：兩者都真，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260917,"parameters":{"P":true,"Q":true,"operator":"∧","context":"P1 與 Q1","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P1 與 Q1\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0002","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P2 與 Q2 的真值分別為 假、真。P2 與 Q2 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P2 與 Q2：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260918,"parameters":{"P":false,"Q":true,"operator":"∧","context":"P2 與 Q2","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P2 與 Q2\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0003","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P3 與 Q3 的真值分別為 真、假。P3 與 Q3 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P3 與 Q3：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260919,"parameters":{"P":true,"Q":false,"operator":"∧","context":"P3 與 Q3","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P3 與 Q3\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0004","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P4 與 Q4 的真值分別為 假、假。P4 與 Q4 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P4 與 Q4：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260920,"parameters":{"P":false,"Q":false,"operator":"∧","context":"P4 與 Q4","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P4 與 Q4\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0005","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P5 與 Q5 的真值分別為 真、真。P5 與 Q5 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P5 與 Q5：兩者都真，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260921,"parameters":{"P":true,"Q":true,"operator":"∧","context":"P5 與 Q5","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P5 與 Q5\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0006","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P6 與 Q6 的真值分別為 假、真。P6 與 Q6 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P6 與 Q6：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260922,"parameters":{"P":false,"Q":true,"operator":"∧","context":"P6 與 Q6","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P6 與 Q6\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0007","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P7 與 Q7 的真值分別為 真、假。P7 與 Q7 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P7 與 Q7：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260923,"parameters":{"P":true,"Q":false,"operator":"∧","context":"P7 與 Q7","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P7 與 Q7\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0008","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P8 與 Q8 的真值分別為 假、假。P8 與 Q8 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P8 與 Q8：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260924,"parameters":{"P":false,"Q":false,"operator":"∧","context":"P8 與 Q8","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P8 與 Q8\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0009","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P9 與 Q9 的真值分別為 真、真。P9 與 Q9 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P9 與 Q9：兩者都真，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260925,"parameters":{"P":true,"Q":true,"operator":"∧","context":"P9 與 Q9","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P9 與 Q9\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0010","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P10 與 Q10 的真值分別為 假、真。P10 與 Q10 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P10 與 Q10：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260926,"parameters":{"P":false,"Q":true,"operator":"∧","context":"P10 與 Q10","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P10 與 Q10\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0011","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P11 與 Q11 的真值分別為 真、假。P11 與 Q11 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P11 與 Q11：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260927,"parameters":{"P":true,"Q":false,"operator":"∧","context":"P11 與 Q11","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P11 與 Q11\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0012","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P12 與 Q12 的真值分別為 假、假。P12 與 Q12 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P12 與 Q12：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260928,"parameters":{"P":false,"Q":false,"operator":"∧","context":"P12 與 Q12","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P12 與 Q12\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0013","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P13 與 Q13 的真值分別為 真、真。P13 與 Q13 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P13 與 Q13：兩者都真，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260929,"parameters":{"P":true,"Q":true,"operator":"∧","context":"P13 與 Q13","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P13 與 Q13\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0014","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P14 與 Q14 的真值分別為 假、真。P14 與 Q14 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P14 與 Q14：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260930,"parameters":{"P":false,"Q":true,"operator":"∧","context":"P14 與 Q14","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P14 與 Q14\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0015","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P15 與 Q15 的真值分別為 真、假。P15 與 Q15 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P15 與 Q15：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260931,"parameters":{"P":true,"Q":false,"operator":"∧","context":"P15 與 Q15","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P15 與 Q15\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0016","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P16 與 Q16 的真值分別為 假、假。P16 與 Q16 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P16 與 Q16：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260932,"parameters":{"P":false,"Q":false,"operator":"∧","context":"P16 與 Q16","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P16 與 Q16\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0017","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P17 與 Q17 的真值分別為 真、真。P17 與 Q17 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P17 與 Q17：兩者都真，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260933,"parameters":{"P":true,"Q":true,"operator":"∧","context":"P17 與 Q17","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P17 與 Q17\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0018","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P18 與 Q18 的真值分別為 假、真。P18 與 Q18 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P18 與 Q18：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260934,"parameters":{"P":false,"Q":true,"operator":"∧","context":"P18 與 Q18","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P18 與 Q18\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0019","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P19 與 Q19 的真值分別為 真、假。P19 與 Q19 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P19 與 Q19：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260935,"parameters":{"P":true,"Q":false,"operator":"∧","context":"P19 與 Q19","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P19 與 Q19\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0020","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P20 與 Q20 的真值分別為 假、假。P20 與 Q20 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P20 與 Q20：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260936,"parameters":{"P":false,"Q":false,"operator":"∧","context":"P20 與 Q20","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P20 與 Q20\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0021","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P21 與 Q21 的真值分別為 真、真。P21 與 Q21 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P21 與 Q21：兩者都真，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260937,"parameters":{"P":true,"Q":true,"operator":"∧","context":"P21 與 Q21","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P21 與 Q21\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0022","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P22 與 Q22 的真值分別為 假、真。P22 與 Q22 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P22 與 Q22：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260938,"parameters":{"P":false,"Q":true,"operator":"∧","context":"P22 與 Q22","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P22 與 Q22\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0023","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P23 與 Q23 的真值分別為 真、假。P23 與 Q23 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P23 與 Q23：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260939,"parameters":{"P":true,"Q":false,"operator":"∧","context":"P23 與 Q23","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P23 與 Q23\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0024","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P24 與 Q24 的真值分別為 假、假。P24 與 Q24 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P24 與 Q24：兩者都真，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260940,"parameters":{"P":false,"Q":false,"operator":"∧","context":"P24 與 Q24","semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P24 與 Q24\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-conjunction-truth-0025","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-conjunction-truth","stem_zh":"指定 P25 與 Q25 的真值分別為 真、真。P25 與 Q25 ∧ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P25 與 Q25：兩者都真，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-conjunction-truth","seed":20260941,"parameters":{"P":true,"Q":true,"operator":"∧","context":"P25 與 Q25","semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P25 與 Q25\",\"operator\":\"∧\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0001","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P1 與 Q1 的真值分別為 真、真。P1 與 Q1 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P1 與 Q1：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261017,"parameters":{"P":true,"Q":true,"operator":"∨","context":"P1 與 Q1","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P1 與 Q1\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0002","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P2 與 Q2 的真值分別為 假、真。P2 與 Q2 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P2 與 Q2：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261018,"parameters":{"P":false,"Q":true,"operator":"∨","context":"P2 與 Q2","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P2 與 Q2\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0003","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P3 與 Q3 的真值分別為 真、假。P3 與 Q3 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P3 與 Q3：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261019,"parameters":{"P":true,"Q":false,"operator":"∨","context":"P3 與 Q3","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P3 與 Q3\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0004","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P4 與 Q4 的真值分別為 假、假。P4 與 Q4 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P4 與 Q4：至少一者真（含括或），故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261020,"parameters":{"P":false,"Q":false,"operator":"∨","context":"P4 與 Q4","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P4 與 Q4\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0005","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P5 與 Q5 的真值分別為 真、真。P5 與 Q5 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P5 與 Q5：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261021,"parameters":{"P":true,"Q":true,"operator":"∨","context":"P5 與 Q5","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P5 與 Q5\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0006","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P6 與 Q6 的真值分別為 假、真。P6 與 Q6 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P6 與 Q6：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261022,"parameters":{"P":false,"Q":true,"operator":"∨","context":"P6 與 Q6","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P6 與 Q6\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0007","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P7 與 Q7 的真值分別為 真、假。P7 與 Q7 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P7 與 Q7：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261023,"parameters":{"P":true,"Q":false,"operator":"∨","context":"P7 與 Q7","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P7 與 Q7\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0008","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P8 與 Q8 的真值分別為 假、假。P8 與 Q8 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P8 與 Q8：至少一者真（含括或），故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261024,"parameters":{"P":false,"Q":false,"operator":"∨","context":"P8 與 Q8","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P8 與 Q8\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0009","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P9 與 Q9 的真值分別為 真、真。P9 與 Q9 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P9 與 Q9：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261025,"parameters":{"P":true,"Q":true,"operator":"∨","context":"P9 與 Q9","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P9 與 Q9\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0010","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P10 與 Q10 的真值分別為 假、真。P10 與 Q10 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P10 與 Q10：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261026,"parameters":{"P":false,"Q":true,"operator":"∨","context":"P10 與 Q10","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P10 與 Q10\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0011","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P11 與 Q11 的真值分別為 真、假。P11 與 Q11 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P11 與 Q11：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261027,"parameters":{"P":true,"Q":false,"operator":"∨","context":"P11 與 Q11","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P11 與 Q11\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0012","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P12 與 Q12 的真值分別為 假、假。P12 與 Q12 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P12 與 Q12：至少一者真（含括或），故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261028,"parameters":{"P":false,"Q":false,"operator":"∨","context":"P12 與 Q12","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P12 與 Q12\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0013","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P13 與 Q13 的真值分別為 真、真。P13 與 Q13 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P13 與 Q13：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261029,"parameters":{"P":true,"Q":true,"operator":"∨","context":"P13 與 Q13","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P13 與 Q13\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0014","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P14 與 Q14 的真值分別為 假、真。P14 與 Q14 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P14 與 Q14：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261030,"parameters":{"P":false,"Q":true,"operator":"∨","context":"P14 與 Q14","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P14 與 Q14\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0015","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P15 與 Q15 的真值分別為 真、假。P15 與 Q15 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P15 與 Q15：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261031,"parameters":{"P":true,"Q":false,"operator":"∨","context":"P15 與 Q15","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P15 與 Q15\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0016","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P16 與 Q16 的真值分別為 假、假。P16 與 Q16 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P16 與 Q16：至少一者真（含括或），故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261032,"parameters":{"P":false,"Q":false,"operator":"∨","context":"P16 與 Q16","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P16 與 Q16\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0017","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P17 與 Q17 的真值分別為 真、真。P17 與 Q17 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P17 與 Q17：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261033,"parameters":{"P":true,"Q":true,"operator":"∨","context":"P17 與 Q17","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P17 與 Q17\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0018","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P18 與 Q18 的真值分別為 假、真。P18 與 Q18 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P18 與 Q18：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261034,"parameters":{"P":false,"Q":true,"operator":"∨","context":"P18 與 Q18","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P18 與 Q18\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0019","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P19 與 Q19 的真值分別為 真、假。P19 與 Q19 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P19 與 Q19：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261035,"parameters":{"P":true,"Q":false,"operator":"∨","context":"P19 與 Q19","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P19 與 Q19\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0020","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P20 與 Q20 的真值分別為 假、假。P20 與 Q20 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P20 與 Q20：至少一者真（含括或），故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261036,"parameters":{"P":false,"Q":false,"operator":"∨","context":"P20 與 Q20","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P20 與 Q20\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0021","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P21 與 Q21 的真值分別為 真、真。P21 與 Q21 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P21 與 Q21：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261037,"parameters":{"P":true,"Q":true,"operator":"∨","context":"P21 與 Q21","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P21 與 Q21\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0022","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P22 與 Q22 的真值分別為 假、真。P22 與 Q22 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P22 與 Q22：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261038,"parameters":{"P":false,"Q":true,"operator":"∨","context":"P22 與 Q22","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P22 與 Q22\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0023","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P23 與 Q23 的真值分別為 真、假。P23 與 Q23 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P23 與 Q23：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261039,"parameters":{"P":true,"Q":false,"operator":"∨","context":"P23 與 Q23","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P23 與 Q23\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0024","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P24 與 Q24 的真值分別為 假、假。P24 與 Q24 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P24 與 Q24：至少一者真（含括或），故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261040,"parameters":{"P":false,"Q":false,"operator":"∨","context":"P24 與 Q24","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P24 與 Q24\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-inclusive-disjunction-truth-0025","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-inclusive-disjunction-truth","stem_zh":"指定 P25 與 Q25 的真值分別為 真、真。P25 與 Q25 ∨ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P25 與 Q25：至少一者真（含括或），故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-inclusive-disjunction-truth","seed":20261041,"parameters":{"P":true,"Q":true,"operator":"∨","context":"P25 與 Q25","semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P25 與 Q25\",\"operator\":\"∨\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0001","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P1 與 Q1 的真值分別為 真、真。P1 與 Q1 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P1 與 Q1：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261117,"parameters":{"P":true,"Q":true,"operator":"→","context":"P1 與 Q1","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P1 與 Q1\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0002","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P2 與 Q2 的真值分別為 假、真。P2 與 Q2 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P2 與 Q2：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261118,"parameters":{"P":false,"Q":true,"operator":"→","context":"P2 與 Q2","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P2 與 Q2\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0003","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P3 與 Q3 的真值分別為 真、假。P3 與 Q3 → 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P3 與 Q3：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261119,"parameters":{"P":true,"Q":false,"operator":"→","context":"P3 與 Q3","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P3 與 Q3\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0004","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P4 與 Q4 的真值分別為 假、假。P4 與 Q4 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P4 與 Q4：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261120,"parameters":{"P":false,"Q":false,"operator":"→","context":"P4 與 Q4","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P4 與 Q4\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0005","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P5 與 Q5 的真值分別為 真、真。P5 與 Q5 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P5 與 Q5：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261121,"parameters":{"P":true,"Q":true,"operator":"→","context":"P5 與 Q5","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P5 與 Q5\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0006","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P6 與 Q6 的真值分別為 假、真。P6 與 Q6 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P6 與 Q6：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261122,"parameters":{"P":false,"Q":true,"operator":"→","context":"P6 與 Q6","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P6 與 Q6\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0007","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P7 與 Q7 的真值分別為 真、假。P7 與 Q7 → 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P7 與 Q7：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261123,"parameters":{"P":true,"Q":false,"operator":"→","context":"P7 與 Q7","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P7 與 Q7\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0008","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P8 與 Q8 的真值分別為 假、假。P8 與 Q8 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P8 與 Q8：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261124,"parameters":{"P":false,"Q":false,"operator":"→","context":"P8 與 Q8","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P8 與 Q8\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0009","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P9 與 Q9 的真值分別為 真、真。P9 與 Q9 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P9 與 Q9：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261125,"parameters":{"P":true,"Q":true,"operator":"→","context":"P9 與 Q9","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P9 與 Q9\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0010","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P10 與 Q10 的真值分別為 假、真。P10 與 Q10 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P10 與 Q10：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261126,"parameters":{"P":false,"Q":true,"operator":"→","context":"P10 與 Q10","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P10 與 Q10\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0011","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P11 與 Q11 的真值分別為 真、假。P11 與 Q11 → 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P11 與 Q11：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261127,"parameters":{"P":true,"Q":false,"operator":"→","context":"P11 與 Q11","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P11 與 Q11\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0012","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P12 與 Q12 的真值分別為 假、假。P12 與 Q12 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P12 與 Q12：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261128,"parameters":{"P":false,"Q":false,"operator":"→","context":"P12 與 Q12","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P12 與 Q12\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0013","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P13 與 Q13 的真值分別為 真、真。P13 與 Q13 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P13 與 Q13：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261129,"parameters":{"P":true,"Q":true,"operator":"→","context":"P13 與 Q13","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P13 與 Q13\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0014","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P14 與 Q14 的真值分別為 假、真。P14 與 Q14 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P14 與 Q14：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261130,"parameters":{"P":false,"Q":true,"operator":"→","context":"P14 與 Q14","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P14 與 Q14\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0015","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P15 與 Q15 的真值分別為 真、假。P15 與 Q15 → 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P15 與 Q15：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261131,"parameters":{"P":true,"Q":false,"operator":"→","context":"P15 與 Q15","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P15 與 Q15\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0016","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P16 與 Q16 的真值分別為 假、假。P16 與 Q16 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P16 與 Q16：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261132,"parameters":{"P":false,"Q":false,"operator":"→","context":"P16 與 Q16","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P16 與 Q16\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0017","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P17 與 Q17 的真值分別為 真、真。P17 與 Q17 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P17 與 Q17：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261133,"parameters":{"P":true,"Q":true,"operator":"→","context":"P17 與 Q17","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P17 與 Q17\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0018","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P18 與 Q18 的真值分別為 假、真。P18 與 Q18 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P18 與 Q18：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261134,"parameters":{"P":false,"Q":true,"operator":"→","context":"P18 與 Q18","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P18 與 Q18\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0019","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P19 與 Q19 的真值分別為 真、假。P19 與 Q19 → 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P19 與 Q19：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261135,"parameters":{"P":true,"Q":false,"operator":"→","context":"P19 與 Q19","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P19 與 Q19\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0020","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P20 與 Q20 的真值分別為 假、假。P20 與 Q20 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P20 與 Q20：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261136,"parameters":{"P":false,"Q":false,"operator":"→","context":"P20 與 Q20","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P20 與 Q20\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0021","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P21 與 Q21 的真值分別為 真、真。P21 與 Q21 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P21 與 Q21：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261137,"parameters":{"P":true,"Q":true,"operator":"→","context":"P21 與 Q21","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P21 與 Q21\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0022","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P22 與 Q22 的真值分別為 假、真。P22 與 Q22 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P22 與 Q22：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261138,"parameters":{"P":false,"Q":true,"operator":"→","context":"P22 與 Q22","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P22 與 Q22\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0023","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P23 與 Q23 的真值分別為 真、假。P23 與 Q23 → 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P23 與 Q23：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261139,"parameters":{"P":true,"Q":false,"operator":"→","context":"P23 與 Q23","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P23 與 Q23\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0024","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P24 與 Q24 的真值分別為 假、假。P24 與 Q24 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P24 與 Q24：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261140,"parameters":{"P":false,"Q":false,"operator":"→","context":"P24 與 Q24","semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P24 與 Q24\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-material-implication-truth-0025","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-material-implication-truth","stem_zh":"指定 P25 與 Q25 的真值分別為 真、真。P25 與 Q25 → 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P25 與 Q25：僅 P 真且 Q 假時為假，非因果敘述，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-material-implication-truth","seed":20261141,"parameters":{"P":true,"Q":true,"operator":"→","context":"P25 與 Q25","semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P25 與 Q25\",\"operator\":\"→\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0001","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P1 與 Q1 的真值分別為 真、真。P1 與 Q1 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P1 與 Q1：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261217,"parameters":{"P":true,"Q":true,"operator":"↔","context":"P1 與 Q1","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P1 與 Q1\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0002","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P2 與 Q2 的真值分別為 假、真。P2 與 Q2 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P2 與 Q2：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261218,"parameters":{"P":false,"Q":true,"operator":"↔","context":"P2 與 Q2","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P2 與 Q2\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0003","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P3 與 Q3 的真值分別為 真、假。P3 與 Q3 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P3 與 Q3：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261219,"parameters":{"P":true,"Q":false,"operator":"↔","context":"P3 與 Q3","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P3 與 Q3\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0004","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P4 與 Q4 的真值分別為 假、假。P4 與 Q4 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P4 與 Q4：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261220,"parameters":{"P":false,"Q":false,"operator":"↔","context":"P4 與 Q4","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P4 與 Q4\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0005","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P5 與 Q5 的真值分別為 真、真。P5 與 Q5 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P5 與 Q5：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261221,"parameters":{"P":true,"Q":true,"operator":"↔","context":"P5 與 Q5","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P5 與 Q5\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0006","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P6 與 Q6 的真值分別為 假、真。P6 與 Q6 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P6 與 Q6：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261222,"parameters":{"P":false,"Q":true,"operator":"↔","context":"P6 與 Q6","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P6 與 Q6\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0007","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P7 與 Q7 的真值分別為 真、假。P7 與 Q7 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P7 與 Q7：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261223,"parameters":{"P":true,"Q":false,"operator":"↔","context":"P7 與 Q7","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P7 與 Q7\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0008","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P8 與 Q8 的真值分別為 假、假。P8 與 Q8 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P8 與 Q8：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261224,"parameters":{"P":false,"Q":false,"operator":"↔","context":"P8 與 Q8","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P8 與 Q8\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0009","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P9 與 Q9 的真值分別為 真、真。P9 與 Q9 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P9 與 Q9：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261225,"parameters":{"P":true,"Q":true,"operator":"↔","context":"P9 與 Q9","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P9 與 Q9\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0010","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P10 與 Q10 的真值分別為 假、真。P10 與 Q10 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P10 與 Q10：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261226,"parameters":{"P":false,"Q":true,"operator":"↔","context":"P10 與 Q10","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P10 與 Q10\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0011","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P11 與 Q11 的真值分別為 真、假。P11 與 Q11 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P11 與 Q11：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261227,"parameters":{"P":true,"Q":false,"operator":"↔","context":"P11 與 Q11","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P11 與 Q11\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0012","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P12 與 Q12 的真值分別為 假、假。P12 與 Q12 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P12 與 Q12：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261228,"parameters":{"P":false,"Q":false,"operator":"↔","context":"P12 與 Q12","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P12 與 Q12\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0013","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P13 與 Q13 的真值分別為 真、真。P13 與 Q13 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P13 與 Q13：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261229,"parameters":{"P":true,"Q":true,"operator":"↔","context":"P13 與 Q13","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P13 與 Q13\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0014","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P14 與 Q14 的真值分別為 假、真。P14 與 Q14 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P14 與 Q14：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261230,"parameters":{"P":false,"Q":true,"operator":"↔","context":"P14 與 Q14","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P14 與 Q14\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0015","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P15 與 Q15 的真值分別為 真、假。P15 與 Q15 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P15 與 Q15：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261231,"parameters":{"P":true,"Q":false,"operator":"↔","context":"P15 與 Q15","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P15 與 Q15\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0016","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P16 與 Q16 的真值分別為 假、假。P16 與 Q16 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P16 與 Q16：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261232,"parameters":{"P":false,"Q":false,"operator":"↔","context":"P16 與 Q16","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P16 與 Q16\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0017","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P17 與 Q17 的真值分別為 真、真。P17 與 Q17 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P17 與 Q17：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261233,"parameters":{"P":true,"Q":true,"operator":"↔","context":"P17 與 Q17","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P17 與 Q17\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0018","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P18 與 Q18 的真值分別為 假、真。P18 與 Q18 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P18 與 Q18：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261234,"parameters":{"P":false,"Q":true,"operator":"↔","context":"P18 與 Q18","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P18 與 Q18\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0019","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P19 與 Q19 的真值分別為 真、假。P19 與 Q19 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P19 與 Q19：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261235,"parameters":{"P":true,"Q":false,"operator":"↔","context":"P19 與 Q19","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P19 與 Q19\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0020","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P20 與 Q20 的真值分別為 假、假。P20 與 Q20 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P20 與 Q20：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261236,"parameters":{"P":false,"Q":false,"operator":"↔","context":"P20 與 Q20","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P20 與 Q20\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0021","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P21 與 Q21 的真值分別為 真、真。P21 與 Q21 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P21 與 Q21：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261237,"parameters":{"P":true,"Q":true,"operator":"↔","context":"P21 與 Q21","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P21 與 Q21\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0022","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P22 與 Q22 的真值分別為 假、真。P22 與 Q22 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P22 與 Q22：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261238,"parameters":{"P":false,"Q":true,"operator":"↔","context":"P22 與 Q22","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P22 與 Q22\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0023","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P23 與 Q23 的真值分別為 真、假。P23 與 Q23 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"P23 與 Q23：兩方向真值相同，故本題值為 假。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261239,"parameters":{"P":true,"Q":false,"operator":"↔","context":"P23 與 Q23","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P23 與 Q23\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0024","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P24 與 Q24 的真值分別為 假、假。P24 與 Q24 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P24 與 Q24：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261240,"parameters":{"P":false,"Q":false,"operator":"↔","context":"P24 與 Q24","semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P24 與 Q24\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260916-logic-biconditional-truth-0025","batch_id":"batch-20260916-logical-connectives","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"qf-logic-biconditional-truth","stem_zh":"指定 P25 與 Q25 的真值分別為 真、真。P25 與 Q25 ↔ 的真值是否為真？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"P25 與 Q25：兩方向真值相同，故本題值為 真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["真值條件","邏輯連接詞"]},"variant":{"family_id":"qf-logic-biconditional-truth","seed":20261241,"parameters":{"P":true,"Q":true,"operator":"↔","context":"P25 與 Q25","semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P25 與 Q25\",\"operator\":\"↔\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-16","contract_version":"ocme-question-factory-v0.1"}}