{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0001","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A=∅、B={-2, 0, 3}，輸入輸出有序對為 []。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"∅","explanation_zh":"定義域為 ∅；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303001,"parameters":{"operation":"domain","A":[],"B":[-2,0,3],"pairs":[],"semantic_template":"qf-function-domain-set/{\"A\":[],\"B\":[-2,0,3],\"operation\":\"domain\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0002","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A=∅、B=∅，輸入輸出有序對為 []。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"∅","explanation_zh":"定義域為 ∅；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303002,"parameters":{"operation":"domain","A":[],"B":[],"pairs":[],"semantic_template":"qf-function-domain-set/{\"A\":[],\"B\":[],\"operation\":\"domain\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0003","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-10, -9, -8, -7}、B={-4, 0, 5}，輸入輸出有序對為 [(-10, 5), (-9, -4), (-8, 0), (-7, 5)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-10, -9, -8, -7}","explanation_zh":"定義域為 {-10, -9, -8, -7}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303003,"parameters":{"operation":"domain","A":[-10,-9,-8,-7],"B":[-4,0,5],"pairs":[[-10,5],[-9,-4],[-8,0],[-7,5]],"semantic_template":"qf-function-domain-set/{\"A\":[-10,-9,-8,-7],\"B\":[-4,0,5],\"operation\":\"domain\",\"pairs\":[[-10,5],[-9,-4],[-8,0],[-7,5]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0004","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-9, -8}、B={-6, 0, 7}，輸入輸出有序對為 [(-9, -6), (-8, 0)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-9, -8}","explanation_zh":"定義域為 {-9, -8}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303004,"parameters":{"operation":"domain","A":[-9,-8],"B":[-6,0,7],"pairs":[[-9,-6],[-8,0]],"semantic_template":"qf-function-domain-set/{\"A\":[-9,-8],\"B\":[-6,0,7],\"operation\":\"domain\",\"pairs\":[[-9,-6],[-8,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0005","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-8, -7, -6}、B={-8, 0, 9}，輸入輸出有序對為 [(-8, 0), (-7, 9), (-6, -8)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-8, -7, -6}","explanation_zh":"定義域為 {-8, -7, -6}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303005,"parameters":{"operation":"domain","A":[-8,-7,-6],"B":[-8,0,9],"pairs":[[-8,0],[-7,9],[-6,-8]],"semantic_template":"qf-function-domain-set/{\"A\":[-8,-7,-6],\"B\":[-8,0,9],\"operation\":\"domain\",\"pairs\":[[-8,0],[-7,9],[-6,-8]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0006","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-7, -6, -5, -4}、B={-10, 0, 11}，輸入輸出有序對為 [(-7, 11), (-6, -10), (-5, 0), (-4, 11)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-7, -6, -5, -4}","explanation_zh":"定義域為 {-7, -6, -5, -4}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303006,"parameters":{"operation":"domain","A":[-7,-6,-5,-4],"B":[-10,0,11],"pairs":[[-7,11],[-6,-10],[-5,0],[-4,11]],"semantic_template":"qf-function-domain-set/{\"A\":[-7,-6,-5,-4],\"B\":[-10,0,11],\"operation\":\"domain\",\"pairs\":[[-7,11],[-6,-10],[-5,0],[-4,11]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0007","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-6, -5}、B={-12, 0, 13}，輸入輸出有序對為 [(-6, -12), (-5, 0)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-6, -5}","explanation_zh":"定義域為 {-6, -5}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303007,"parameters":{"operation":"domain","A":[-6,-5],"B":[-12,0,13],"pairs":[[-6,-12],[-5,0]],"semantic_template":"qf-function-domain-set/{\"A\":[-6,-5],\"B\":[-12,0,13],\"operation\":\"domain\",\"pairs\":[[-6,-12],[-5,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0008","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-5, -4, -3}、B={-14, 0, 15}，輸入輸出有序對為 [(-5, 0), (-4, 15), (-3, -14)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-5, -4, -3}","explanation_zh":"定義域為 {-5, -4, -3}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303008,"parameters":{"operation":"domain","A":[-5,-4,-3],"B":[-14,0,15],"pairs":[[-5,0],[-4,15],[-3,-14]],"semantic_template":"qf-function-domain-set/{\"A\":[-5,-4,-3],\"B\":[-14,0,15],\"operation\":\"domain\",\"pairs\":[[-5,0],[-4,15],[-3,-14]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0009","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-4, -3, -2, -1}、B={-16, 0, 17}，輸入輸出有序對為 [(-4, 17), (-3, -16), (-2, 0), (-1, 17)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-4, -3, -2, -1}","explanation_zh":"定義域為 {-4, -3, -2, -1}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303009,"parameters":{"operation":"domain","A":[-4,-3,-2,-1],"B":[-16,0,17],"pairs":[[-4,17],[-3,-16],[-2,0],[-1,17]],"semantic_template":"qf-function-domain-set/{\"A\":[-4,-3,-2,-1],\"B\":[-16,0,17],\"operation\":\"domain\",\"pairs\":[[-4,17],[-3,-16],[-2,0],[-1,17]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0010","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-3, -2}、B={-18, 0, 19}，輸入輸出有序對為 [(-3, -18), (-2, 0)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-3, -2}","explanation_zh":"定義域為 {-3, -2}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303010,"parameters":{"operation":"domain","A":[-3,-2],"B":[-18,0,19],"pairs":[[-3,-18],[-2,0]],"semantic_template":"qf-function-domain-set/{\"A\":[-3,-2],\"B\":[-18,0,19],\"operation\":\"domain\",\"pairs\":[[-3,-18],[-2,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0011","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-2, -1, 0}、B={-20, 0, 21}，輸入輸出有序對為 [(-2, 0), (-1, 21), (0, -20)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-2, -1, 0}","explanation_zh":"定義域為 {-2, -1, 0}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303011,"parameters":{"operation":"domain","A":[-2,-1,0],"B":[-20,0,21],"pairs":[[-2,0],[-1,21],[0,-20]],"semantic_template":"qf-function-domain-set/{\"A\":[-2,-1,0],\"B\":[-20,0,21],\"operation\":\"domain\",\"pairs\":[[-2,0],[-1,21],[0,-20]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0012","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={-1, 0, 1, 2}、B={-22, 0, 23}，輸入輸出有序對為 [(-1, 23), (0, -22), (1, 0), (2, 23)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-1, 0, 1, 2}","explanation_zh":"定義域為 {-1, 0, 1, 2}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303012,"parameters":{"operation":"domain","A":[-1,0,1,2],"B":[-22,0,23],"pairs":[[-1,23],[0,-22],[1,0],[2,23]],"semantic_template":"qf-function-domain-set/{\"A\":[-1,0,1,2],\"B\":[-22,0,23],\"operation\":\"domain\",\"pairs\":[[-1,23],[0,-22],[1,0],[2,23]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0013","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={0, 1}、B={-24, 0, 25}，輸入輸出有序對為 [(0, -24), (1, 0)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{0, 1}","explanation_zh":"定義域為 {0, 1}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303013,"parameters":{"operation":"domain","A":[0,1],"B":[-24,0,25],"pairs":[[0,-24],[1,0]],"semantic_template":"qf-function-domain-set/{\"A\":[0,1],\"B\":[-24,0,25],\"operation\":\"domain\",\"pairs\":[[0,-24],[1,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0014","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={1, 2, 3}、B={-26, 0, 27}，輸入輸出有序對為 [(1, 0), (2, 27), (3, -26)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{1, 2, 3}","explanation_zh":"定義域為 {1, 2, 3}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303014,"parameters":{"operation":"domain","A":[1,2,3],"B":[-26,0,27],"pairs":[[1,0],[2,27],[3,-26]],"semantic_template":"qf-function-domain-set/{\"A\":[1,2,3],\"B\":[-26,0,27],\"operation\":\"domain\",\"pairs\":[[1,0],[2,27],[3,-26]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0015","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={2, 3, 4, 5}、B={-28, 0, 29}，輸入輸出有序對為 [(2, 29), (3, -28), (4, 0), (5, 29)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{2, 3, 4, 5}","explanation_zh":"定義域為 {2, 3, 4, 5}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303015,"parameters":{"operation":"domain","A":[2,3,4,5],"B":[-28,0,29],"pairs":[[2,29],[3,-28],[4,0],[5,29]],"semantic_template":"qf-function-domain-set/{\"A\":[2,3,4,5],\"B\":[-28,0,29],\"operation\":\"domain\",\"pairs\":[[2,29],[3,-28],[4,0],[5,29]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0016","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={3, 4}、B={-30, 0, 31}，輸入輸出有序對為 [(3, -30), (4, 0)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{3, 4}","explanation_zh":"定義域為 {3, 4}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303016,"parameters":{"operation":"domain","A":[3,4],"B":[-30,0,31],"pairs":[[3,-30],[4,0]],"semantic_template":"qf-function-domain-set/{\"A\":[3,4],\"B\":[-30,0,31],\"operation\":\"domain\",\"pairs\":[[3,-30],[4,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0017","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={4, 5, 6}、B={-32, 0, 33}，輸入輸出有序對為 [(4, 0), (5, 33), (6, -32)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{4, 5, 6}","explanation_zh":"定義域為 {4, 5, 6}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303017,"parameters":{"operation":"domain","A":[4,5,6],"B":[-32,0,33],"pairs":[[4,0],[5,33],[6,-32]],"semantic_template":"qf-function-domain-set/{\"A\":[4,5,6],\"B\":[-32,0,33],\"operation\":\"domain\",\"pairs\":[[4,0],[5,33],[6,-32]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0018","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={5, 6, 7, 8}、B={-34, 0, 35}，輸入輸出有序對為 [(5, 35), (6, -34), (7, 0), (8, 35)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{5, 6, 7, 8}","explanation_zh":"定義域為 {5, 6, 7, 8}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303018,"parameters":{"operation":"domain","A":[5,6,7,8],"B":[-34,0,35],"pairs":[[5,35],[6,-34],[7,0],[8,35]],"semantic_template":"qf-function-domain-set/{\"A\":[5,6,7,8],\"B\":[-34,0,35],\"operation\":\"domain\",\"pairs\":[[5,35],[6,-34],[7,0],[8,35]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0019","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={6, 7}、B={-36, 0, 37}，輸入輸出有序對為 [(6, -36), (7, 0)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{6, 7}","explanation_zh":"定義域為 {6, 7}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303019,"parameters":{"operation":"domain","A":[6,7],"B":[-36,0,37],"pairs":[[6,-36],[7,0]],"semantic_template":"qf-function-domain-set/{\"A\":[6,7],\"B\":[-36,0,37],\"operation\":\"domain\",\"pairs\":[[6,-36],[7,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0020","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={7, 8, 9}、B={-38, 0, 39}，輸入輸出有序對為 [(7, 0), (8, 39), (9, -38)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{7, 8, 9}","explanation_zh":"定義域為 {7, 8, 9}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303020,"parameters":{"operation":"domain","A":[7,8,9],"B":[-38,0,39],"pairs":[[7,0],[8,39],[9,-38]],"semantic_template":"qf-function-domain-set/{\"A\":[7,8,9],\"B\":[-38,0,39],\"operation\":\"domain\",\"pairs\":[[7,0],[8,39],[9,-38]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0021","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={8, 9, 10, 11}、B={-40, 0, 41}，輸入輸出有序對為 [(8, 41), (9, -40), (10, 0), (11, 41)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{8, 9, 10, 11}","explanation_zh":"定義域為 {8, 9, 10, 11}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303021,"parameters":{"operation":"domain","A":[8,9,10,11],"B":[-40,0,41],"pairs":[[8,41],[9,-40],[10,0],[11,41]],"semantic_template":"qf-function-domain-set/{\"A\":[8,9,10,11],\"B\":[-40,0,41],\"operation\":\"domain\",\"pairs\":[[8,41],[9,-40],[10,0],[11,41]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0022","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={9, 10}、B={-42, 0, 43}，輸入輸出有序對為 [(9, -42), (10, 0)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{9, 10}","explanation_zh":"定義域為 {9, 10}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303022,"parameters":{"operation":"domain","A":[9,10],"B":[-42,0,43],"pairs":[[9,-42],[10,0]],"semantic_template":"qf-function-domain-set/{\"A\":[9,10],\"B\":[-42,0,43],\"operation\":\"domain\",\"pairs\":[[9,-42],[10,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0023","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={10, 11, 12}、B={-44, 0, 45}，輸入輸出有序對為 [(10, 0), (11, 45), (12, -44)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{10, 11, 12}","explanation_zh":"定義域為 {10, 11, 12}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303023,"parameters":{"operation":"domain","A":[10,11,12],"B":[-44,0,45],"pairs":[[10,0],[11,45],[12,-44]],"semantic_template":"qf-function-domain-set/{\"A\":[10,11,12],\"B\":[-44,0,45],\"operation\":\"domain\",\"pairs\":[[10,0],[11,45],[12,-44]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0024","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={11, 12, 13, 14}、B={-46, 0, 47}，輸入輸出有序對為 [(11, 47), (12, -46), (13, 0), (14, 47)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{11, 12, 13, 14}","explanation_zh":"定義域為 {11, 12, 13, 14}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303024,"parameters":{"operation":"domain","A":[11,12,13,14],"B":[-46,0,47],"pairs":[[11,47],[12,-46],[13,0],[14,47]],"semantic_template":"qf-function-domain-set/{\"A\":[11,12,13,14],\"B\":[-46,0,47],\"operation\":\"domain\",\"pairs\":[[11,47],[12,-46],[13,0],[14,47]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-domain-set-0025","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數定義域","stem_zh":"明示 A={12, 13}、B={-48, 0, 49}，輸入輸出有序對為 [(12, -48), (13, 0)]。已知它是總函數 f:A→B，請列出定義域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{12, 13}","explanation_zh":"定義域為 {12, 13}；直接使用明示宣告的 A，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示集合","總函數"]},"variant":{"family_id":"qf-function-domain-set","seed":202609303025,"parameters":{"operation":"domain","A":[12,13],"B":[-48,0,49],"pairs":[[12,-48],[13,0]],"semantic_template":"qf-function-domain-set/{\"A\":[12,13],\"B\":[-48,0,49],\"operation\":\"domain\",\"pairs\":[[12,-48],[13,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0001","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A=∅、B={-2, 0, 3}，輸入輸出有序對為 []。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-2, 0, 3}","explanation_zh":"陪域為 {-2, 0, 3}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303101,"parameters":{"operation":"codomain","A":[],"B":[-2,0,3],"pairs":[],"semantic_template":"qf-function-codomain-set/{\"A\":[],\"B\":[-2,0,3],\"operation\":\"codomain\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0002","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A=∅、B=∅，輸入輸出有序對為 []。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"∅","explanation_zh":"陪域為 ∅；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303102,"parameters":{"operation":"codomain","A":[],"B":[],"pairs":[],"semantic_template":"qf-function-codomain-set/{\"A\":[],\"B\":[],\"operation\":\"codomain\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0003","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-10, -9, -8, -7}、B={-4, 0, 5}，輸入輸出有序對為 [(-10, 5), (-9, -4), (-8, 0), (-7, 5)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-4, 0, 5}","explanation_zh":"陪域為 {-4, 0, 5}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303103,"parameters":{"operation":"codomain","A":[-10,-9,-8,-7],"B":[-4,0,5],"pairs":[[-10,5],[-9,-4],[-8,0],[-7,5]],"semantic_template":"qf-function-codomain-set/{\"A\":[-10,-9,-8,-7],\"B\":[-4,0,5],\"operation\":\"codomain\",\"pairs\":[[-10,5],[-9,-4],[-8,0],[-7,5]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0004","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-9, -8}、B={-6, 0, 7}，輸入輸出有序對為 [(-9, -6), (-8, 0)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-6, 0, 7}","explanation_zh":"陪域為 {-6, 0, 7}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303104,"parameters":{"operation":"codomain","A":[-9,-8],"B":[-6,0,7],"pairs":[[-9,-6],[-8,0]],"semantic_template":"qf-function-codomain-set/{\"A\":[-9,-8],\"B\":[-6,0,7],\"operation\":\"codomain\",\"pairs\":[[-9,-6],[-8,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0005","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-8, -7, -6}、B={-8, 0, 9}，輸入輸出有序對為 [(-8, 0), (-7, 9), (-6, -8)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-8, 0, 9}","explanation_zh":"陪域為 {-8, 0, 9}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303105,"parameters":{"operation":"codomain","A":[-8,-7,-6],"B":[-8,0,9],"pairs":[[-8,0],[-7,9],[-6,-8]],"semantic_template":"qf-function-codomain-set/{\"A\":[-8,-7,-6],\"B\":[-8,0,9],\"operation\":\"codomain\",\"pairs\":[[-8,0],[-7,9],[-6,-8]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0006","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-7, -6, -5, -4}、B={-10, 0, 11}，輸入輸出有序對為 [(-7, 11), (-6, -10), (-5, 0), (-4, 11)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-10, 0, 11}","explanation_zh":"陪域為 {-10, 0, 11}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303106,"parameters":{"operation":"codomain","A":[-7,-6,-5,-4],"B":[-10,0,11],"pairs":[[-7,11],[-6,-10],[-5,0],[-4,11]],"semantic_template":"qf-function-codomain-set/{\"A\":[-7,-6,-5,-4],\"B\":[-10,0,11],\"operation\":\"codomain\",\"pairs\":[[-7,11],[-6,-10],[-5,0],[-4,11]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0007","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-6, -5}、B={-12, 0, 13}，輸入輸出有序對為 [(-6, -12), (-5, 0)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-12, 0, 13}","explanation_zh":"陪域為 {-12, 0, 13}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303107,"parameters":{"operation":"codomain","A":[-6,-5],"B":[-12,0,13],"pairs":[[-6,-12],[-5,0]],"semantic_template":"qf-function-codomain-set/{\"A\":[-6,-5],\"B\":[-12,0,13],\"operation\":\"codomain\",\"pairs\":[[-6,-12],[-5,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0008","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-5, -4, -3}、B={-14, 0, 15}，輸入輸出有序對為 [(-5, 0), (-4, 15), (-3, -14)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-14, 0, 15}","explanation_zh":"陪域為 {-14, 0, 15}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303108,"parameters":{"operation":"codomain","A":[-5,-4,-3],"B":[-14,0,15],"pairs":[[-5,0],[-4,15],[-3,-14]],"semantic_template":"qf-function-codomain-set/{\"A\":[-5,-4,-3],\"B\":[-14,0,15],\"operation\":\"codomain\",\"pairs\":[[-5,0],[-4,15],[-3,-14]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0009","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-4, -3, -2, -1}、B={-16, 0, 17}，輸入輸出有序對為 [(-4, 17), (-3, -16), (-2, 0), (-1, 17)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-16, 0, 17}","explanation_zh":"陪域為 {-16, 0, 17}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303109,"parameters":{"operation":"codomain","A":[-4,-3,-2,-1],"B":[-16,0,17],"pairs":[[-4,17],[-3,-16],[-2,0],[-1,17]],"semantic_template":"qf-function-codomain-set/{\"A\":[-4,-3,-2,-1],\"B\":[-16,0,17],\"operation\":\"codomain\",\"pairs\":[[-4,17],[-3,-16],[-2,0],[-1,17]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0010","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-3, -2}、B={-18, 0, 19}，輸入輸出有序對為 [(-3, -18), (-2, 0)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-18, 0, 19}","explanation_zh":"陪域為 {-18, 0, 19}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303110,"parameters":{"operation":"codomain","A":[-3,-2],"B":[-18,0,19],"pairs":[[-3,-18],[-2,0]],"semantic_template":"qf-function-codomain-set/{\"A\":[-3,-2],\"B\":[-18,0,19],\"operation\":\"codomain\",\"pairs\":[[-3,-18],[-2,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0011","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-2, -1, 0}、B={-20, 0, 21}，輸入輸出有序對為 [(-2, 0), (-1, 21), (0, -20)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-20, 0, 21}","explanation_zh":"陪域為 {-20, 0, 21}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303111,"parameters":{"operation":"codomain","A":[-2,-1,0],"B":[-20,0,21],"pairs":[[-2,0],[-1,21],[0,-20]],"semantic_template":"qf-function-codomain-set/{\"A\":[-2,-1,0],\"B\":[-20,0,21],\"operation\":\"codomain\",\"pairs\":[[-2,0],[-1,21],[0,-20]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0012","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={-1, 0, 1, 2}、B={-22, 0, 23}，輸入輸出有序對為 [(-1, 23), (0, -22), (1, 0), (2, 23)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-22, 0, 23}","explanation_zh":"陪域為 {-22, 0, 23}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303112,"parameters":{"operation":"codomain","A":[-1,0,1,2],"B":[-22,0,23],"pairs":[[-1,23],[0,-22],[1,0],[2,23]],"semantic_template":"qf-function-codomain-set/{\"A\":[-1,0,1,2],\"B\":[-22,0,23],\"operation\":\"codomain\",\"pairs\":[[-1,23],[0,-22],[1,0],[2,23]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0013","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={0, 1}、B={-24, 0, 25}，輸入輸出有序對為 [(0, -24), (1, 0)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-24, 0, 25}","explanation_zh":"陪域為 {-24, 0, 25}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303113,"parameters":{"operation":"codomain","A":[0,1],"B":[-24,0,25],"pairs":[[0,-24],[1,0]],"semantic_template":"qf-function-codomain-set/{\"A\":[0,1],\"B\":[-24,0,25],\"operation\":\"codomain\",\"pairs\":[[0,-24],[1,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0014","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={1, 2, 3}、B={-26, 0, 27}，輸入輸出有序對為 [(1, 0), (2, 27), (3, -26)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-26, 0, 27}","explanation_zh":"陪域為 {-26, 0, 27}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303114,"parameters":{"operation":"codomain","A":[1,2,3],"B":[-26,0,27],"pairs":[[1,0],[2,27],[3,-26]],"semantic_template":"qf-function-codomain-set/{\"A\":[1,2,3],\"B\":[-26,0,27],\"operation\":\"codomain\",\"pairs\":[[1,0],[2,27],[3,-26]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0015","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={2, 3, 4, 5}、B={-28, 0, 29}，輸入輸出有序對為 [(2, 29), (3, -28), (4, 0), (5, 29)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-28, 0, 29}","explanation_zh":"陪域為 {-28, 0, 29}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303115,"parameters":{"operation":"codomain","A":[2,3,4,5],"B":[-28,0,29],"pairs":[[2,29],[3,-28],[4,0],[5,29]],"semantic_template":"qf-function-codomain-set/{\"A\":[2,3,4,5],\"B\":[-28,0,29],\"operation\":\"codomain\",\"pairs\":[[2,29],[3,-28],[4,0],[5,29]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0016","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={3, 4}、B={-30, 0, 31}，輸入輸出有序對為 [(3, -30), (4, 0)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-30, 0, 31}","explanation_zh":"陪域為 {-30, 0, 31}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303116,"parameters":{"operation":"codomain","A":[3,4],"B":[-30,0,31],"pairs":[[3,-30],[4,0]],"semantic_template":"qf-function-codomain-set/{\"A\":[3,4],\"B\":[-30,0,31],\"operation\":\"codomain\",\"pairs\":[[3,-30],[4,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0017","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={4, 5, 6}、B={-32, 0, 33}，輸入輸出有序對為 [(4, 0), (5, 33), (6, -32)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-32, 0, 33}","explanation_zh":"陪域為 {-32, 0, 33}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303117,"parameters":{"operation":"codomain","A":[4,5,6],"B":[-32,0,33],"pairs":[[4,0],[5,33],[6,-32]],"semantic_template":"qf-function-codomain-set/{\"A\":[4,5,6],\"B\":[-32,0,33],\"operation\":\"codomain\",\"pairs\":[[4,0],[5,33],[6,-32]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0018","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={5, 6, 7, 8}、B={-34, 0, 35}，輸入輸出有序對為 [(5, 35), (6, -34), (7, 0), (8, 35)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-34, 0, 35}","explanation_zh":"陪域為 {-34, 0, 35}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303118,"parameters":{"operation":"codomain","A":[5,6,7,8],"B":[-34,0,35],"pairs":[[5,35],[6,-34],[7,0],[8,35]],"semantic_template":"qf-function-codomain-set/{\"A\":[5,6,7,8],\"B\":[-34,0,35],\"operation\":\"codomain\",\"pairs\":[[5,35],[6,-34],[7,0],[8,35]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0019","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={6, 7}、B={-36, 0, 37}，輸入輸出有序對為 [(6, -36), (7, 0)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-36, 0, 37}","explanation_zh":"陪域為 {-36, 0, 37}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303119,"parameters":{"operation":"codomain","A":[6,7],"B":[-36,0,37],"pairs":[[6,-36],[7,0]],"semantic_template":"qf-function-codomain-set/{\"A\":[6,7],\"B\":[-36,0,37],\"operation\":\"codomain\",\"pairs\":[[6,-36],[7,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0020","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={7, 8, 9}、B={-38, 0, 39}，輸入輸出有序對為 [(7, 0), (8, 39), (9, -38)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-38, 0, 39}","explanation_zh":"陪域為 {-38, 0, 39}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303120,"parameters":{"operation":"codomain","A":[7,8,9],"B":[-38,0,39],"pairs":[[7,0],[8,39],[9,-38]],"semantic_template":"qf-function-codomain-set/{\"A\":[7,8,9],\"B\":[-38,0,39],\"operation\":\"codomain\",\"pairs\":[[7,0],[8,39],[9,-38]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0021","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={8, 9, 10, 11}、B={-40, 0, 41}，輸入輸出有序對為 [(8, 41), (9, -40), (10, 0), (11, 41)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-40, 0, 41}","explanation_zh":"陪域為 {-40, 0, 41}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303121,"parameters":{"operation":"codomain","A":[8,9,10,11],"B":[-40,0,41],"pairs":[[8,41],[9,-40],[10,0],[11,41]],"semantic_template":"qf-function-codomain-set/{\"A\":[8,9,10,11],\"B\":[-40,0,41],\"operation\":\"codomain\",\"pairs\":[[8,41],[9,-40],[10,0],[11,41]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0022","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={9, 10}、B={-42, 0, 43}，輸入輸出有序對為 [(9, -42), (10, 0)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-42, 0, 43}","explanation_zh":"陪域為 {-42, 0, 43}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303122,"parameters":{"operation":"codomain","A":[9,10],"B":[-42,0,43],"pairs":[[9,-42],[10,0]],"semantic_template":"qf-function-codomain-set/{\"A\":[9,10],\"B\":[-42,0,43],\"operation\":\"codomain\",\"pairs\":[[9,-42],[10,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0023","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={10, 11, 12}、B={-44, 0, 45}，輸入輸出有序對為 [(10, 0), (11, 45), (12, -44)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-44, 0, 45}","explanation_zh":"陪域為 {-44, 0, 45}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303123,"parameters":{"operation":"codomain","A":[10,11,12],"B":[-44,0,45],"pairs":[[10,0],[11,45],[12,-44]],"semantic_template":"qf-function-codomain-set/{\"A\":[10,11,12],\"B\":[-44,0,45],\"operation\":\"codomain\",\"pairs\":[[10,0],[11,45],[12,-44]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0024","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={11, 12, 13, 14}、B={-46, 0, 47}，輸入輸出有序對為 [(11, 47), (12, -46), (13, 0), (14, 47)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-46, 0, 47}","explanation_zh":"陪域為 {-46, 0, 47}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303124,"parameters":{"operation":"codomain","A":[11,12,13,14],"B":[-46,0,47],"pairs":[[11,47],[12,-46],[13,0],[14,47]],"semantic_template":"qf-function-codomain-set/{\"A\":[11,12,13,14],\"B\":[-46,0,47],\"operation\":\"codomain\",\"pairs\":[[11,47],[12,-46],[13,0],[14,47]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-codomain-set-0025","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數陪域","stem_zh":"明示 A={12, 13}、B={-48, 0, 49}，輸入輸出有序對為 [(12, -48), (13, 0)]。已知它是總函數 f:A→B，請列出陪域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-48, 0, 49}","explanation_zh":"陪域為 {-48, 0, 49}；直接使用明示宣告的 B，不從輸出表猜測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["宣告陪域","總函數"]},"variant":{"family_id":"qf-function-codomain-set","seed":202609303125,"parameters":{"operation":"codomain","A":[12,13],"B":[-48,0,49],"pairs":[[12,-48],[13,0]],"semantic_template":"qf-function-codomain-set/{\"A\":[12,13],\"B\":[-48,0,49],\"operation\":\"codomain\",\"pairs\":[[12,-48],[13,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0001","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A=∅、B={-2, 0, 3}，輸入輸出有序對為 []。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"∅","explanation_zh":"值域為 ∅；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303201,"parameters":{"operation":"range","A":[],"B":[-2,0,3],"pairs":[],"semantic_template":"qf-function-range-set/{\"A\":[],\"B\":[-2,0,3],\"operation\":\"range\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0002","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A=∅、B=∅，輸入輸出有序對為 []。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"∅","explanation_zh":"值域為 ∅；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303202,"parameters":{"operation":"range","A":[],"B":[],"pairs":[],"semantic_template":"qf-function-range-set/{\"A\":[],\"B\":[],\"operation\":\"range\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0003","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-10, -9, -8, -7}、B={-4, 0, 5}，輸入輸出有序對為 [(-10, 5), (-9, -4), (-8, 0), (-7, 5)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-4, 0, 5}","explanation_zh":"值域為 {-4, 0, 5}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303203,"parameters":{"operation":"range","A":[-10,-9,-8,-7],"B":[-4,0,5],"pairs":[[-10,5],[-9,-4],[-8,0],[-7,5]],"semantic_template":"qf-function-range-set/{\"A\":[-10,-9,-8,-7],\"B\":[-4,0,5],\"operation\":\"range\",\"pairs\":[[-10,5],[-9,-4],[-8,0],[-7,5]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0004","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-9, -8}、B={-6, 0, 7}，輸入輸出有序對為 [(-9, -6), (-8, 0)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-6, 0}","explanation_zh":"值域為 {-6, 0}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303204,"parameters":{"operation":"range","A":[-9,-8],"B":[-6,0,7],"pairs":[[-9,-6],[-8,0]],"semantic_template":"qf-function-range-set/{\"A\":[-9,-8],\"B\":[-6,0,7],\"operation\":\"range\",\"pairs\":[[-9,-6],[-8,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0005","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-8, -7, -6}、B={-8, 0, 9}，輸入輸出有序對為 [(-8, 0), (-7, 9), (-6, -8)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-8, 0, 9}","explanation_zh":"值域為 {-8, 0, 9}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303205,"parameters":{"operation":"range","A":[-8,-7,-6],"B":[-8,0,9],"pairs":[[-8,0],[-7,9],[-6,-8]],"semantic_template":"qf-function-range-set/{\"A\":[-8,-7,-6],\"B\":[-8,0,9],\"operation\":\"range\",\"pairs\":[[-8,0],[-7,9],[-6,-8]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0006","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-7, -6, -5, -4}、B={-10, 0, 11}，輸入輸出有序對為 [(-7, 11), (-6, -10), (-5, 0), (-4, 11)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-10, 0, 11}","explanation_zh":"值域為 {-10, 0, 11}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303206,"parameters":{"operation":"range","A":[-7,-6,-5,-4],"B":[-10,0,11],"pairs":[[-7,11],[-6,-10],[-5,0],[-4,11]],"semantic_template":"qf-function-range-set/{\"A\":[-7,-6,-5,-4],\"B\":[-10,0,11],\"operation\":\"range\",\"pairs\":[[-7,11],[-6,-10],[-5,0],[-4,11]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0007","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-6, -5}、B={-12, 0, 13}，輸入輸出有序對為 [(-6, -12), (-5, 0)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-12, 0}","explanation_zh":"值域為 {-12, 0}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303207,"parameters":{"operation":"range","A":[-6,-5],"B":[-12,0,13],"pairs":[[-6,-12],[-5,0]],"semantic_template":"qf-function-range-set/{\"A\":[-6,-5],\"B\":[-12,0,13],\"operation\":\"range\",\"pairs\":[[-6,-12],[-5,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0008","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-5, -4, -3}、B={-14, 0, 15}，輸入輸出有序對為 [(-5, 0), (-4, 15), (-3, -14)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-14, 0, 15}","explanation_zh":"值域為 {-14, 0, 15}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303208,"parameters":{"operation":"range","A":[-5,-4,-3],"B":[-14,0,15],"pairs":[[-5,0],[-4,15],[-3,-14]],"semantic_template":"qf-function-range-set/{\"A\":[-5,-4,-3],\"B\":[-14,0,15],\"operation\":\"range\",\"pairs\":[[-5,0],[-4,15],[-3,-14]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0009","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-4, -3, -2, -1}、B={-16, 0, 17}，輸入輸出有序對為 [(-4, 17), (-3, -16), (-2, 0), (-1, 17)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-16, 0, 17}","explanation_zh":"值域為 {-16, 0, 17}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303209,"parameters":{"operation":"range","A":[-4,-3,-2,-1],"B":[-16,0,17],"pairs":[[-4,17],[-3,-16],[-2,0],[-1,17]],"semantic_template":"qf-function-range-set/{\"A\":[-4,-3,-2,-1],\"B\":[-16,0,17],\"operation\":\"range\",\"pairs\":[[-4,17],[-3,-16],[-2,0],[-1,17]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0010","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-3, -2}、B={-18, 0, 19}，輸入輸出有序對為 [(-3, -18), (-2, 0)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-18, 0}","explanation_zh":"值域為 {-18, 0}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303210,"parameters":{"operation":"range","A":[-3,-2],"B":[-18,0,19],"pairs":[[-3,-18],[-2,0]],"semantic_template":"qf-function-range-set/{\"A\":[-3,-2],\"B\":[-18,0,19],\"operation\":\"range\",\"pairs\":[[-3,-18],[-2,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0011","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-2, -1, 0}、B={-20, 0, 21}，輸入輸出有序對為 [(-2, 0), (-1, 21), (0, -20)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-20, 0, 21}","explanation_zh":"值域為 {-20, 0, 21}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303211,"parameters":{"operation":"range","A":[-2,-1,0],"B":[-20,0,21],"pairs":[[-2,0],[-1,21],[0,-20]],"semantic_template":"qf-function-range-set/{\"A\":[-2,-1,0],\"B\":[-20,0,21],\"operation\":\"range\",\"pairs\":[[-2,0],[-1,21],[0,-20]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0012","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={-1, 0, 1, 2}、B={-22, 0, 23}，輸入輸出有序對為 [(-1, 23), (0, -22), (1, 0), (2, 23)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-22, 0, 23}","explanation_zh":"值域為 {-22, 0, 23}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303212,"parameters":{"operation":"range","A":[-1,0,1,2],"B":[-22,0,23],"pairs":[[-1,23],[0,-22],[1,0],[2,23]],"semantic_template":"qf-function-range-set/{\"A\":[-1,0,1,2],\"B\":[-22,0,23],\"operation\":\"range\",\"pairs\":[[-1,23],[0,-22],[1,0],[2,23]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0013","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={0, 1}、B={-24, 0, 25}，輸入輸出有序對為 [(0, -24), (1, 0)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-24, 0}","explanation_zh":"值域為 {-24, 0}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303213,"parameters":{"operation":"range","A":[0,1],"B":[-24,0,25],"pairs":[[0,-24],[1,0]],"semantic_template":"qf-function-range-set/{\"A\":[0,1],\"B\":[-24,0,25],\"operation\":\"range\",\"pairs\":[[0,-24],[1,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0014","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={1, 2, 3}、B={-26, 0, 27}，輸入輸出有序對為 [(1, 0), (2, 27), (3, -26)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-26, 0, 27}","explanation_zh":"值域為 {-26, 0, 27}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303214,"parameters":{"operation":"range","A":[1,2,3],"B":[-26,0,27],"pairs":[[1,0],[2,27],[3,-26]],"semantic_template":"qf-function-range-set/{\"A\":[1,2,3],\"B\":[-26,0,27],\"operation\":\"range\",\"pairs\":[[1,0],[2,27],[3,-26]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0015","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={2, 3, 4, 5}、B={-28, 0, 29}，輸入輸出有序對為 [(2, 29), (3, -28), (4, 0), (5, 29)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-28, 0, 29}","explanation_zh":"值域為 {-28, 0, 29}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303215,"parameters":{"operation":"range","A":[2,3,4,5],"B":[-28,0,29],"pairs":[[2,29],[3,-28],[4,0],[5,29]],"semantic_template":"qf-function-range-set/{\"A\":[2,3,4,5],\"B\":[-28,0,29],\"operation\":\"range\",\"pairs\":[[2,29],[3,-28],[4,0],[5,29]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0016","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={3, 4}、B={-30, 0, 31}，輸入輸出有序對為 [(3, -30), (4, 0)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-30, 0}","explanation_zh":"值域為 {-30, 0}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303216,"parameters":{"operation":"range","A":[3,4],"B":[-30,0,31],"pairs":[[3,-30],[4,0]],"semantic_template":"qf-function-range-set/{\"A\":[3,4],\"B\":[-30,0,31],\"operation\":\"range\",\"pairs\":[[3,-30],[4,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0017","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={4, 5, 6}、B={-32, 0, 33}，輸入輸出有序對為 [(4, 0), (5, 33), (6, -32)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-32, 0, 33}","explanation_zh":"值域為 {-32, 0, 33}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303217,"parameters":{"operation":"range","A":[4,5,6],"B":[-32,0,33],"pairs":[[4,0],[5,33],[6,-32]],"semantic_template":"qf-function-range-set/{\"A\":[4,5,6],\"B\":[-32,0,33],\"operation\":\"range\",\"pairs\":[[4,0],[5,33],[6,-32]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0018","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={5, 6, 7, 8}、B={-34, 0, 35}，輸入輸出有序對為 [(5, 35), (6, -34), (7, 0), (8, 35)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-34, 0, 35}","explanation_zh":"值域為 {-34, 0, 35}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303218,"parameters":{"operation":"range","A":[5,6,7,8],"B":[-34,0,35],"pairs":[[5,35],[6,-34],[7,0],[8,35]],"semantic_template":"qf-function-range-set/{\"A\":[5,6,7,8],\"B\":[-34,0,35],\"operation\":\"range\",\"pairs\":[[5,35],[6,-34],[7,0],[8,35]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0019","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={6, 7}、B={-36, 0, 37}，輸入輸出有序對為 [(6, -36), (7, 0)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-36, 0}","explanation_zh":"值域為 {-36, 0}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303219,"parameters":{"operation":"range","A":[6,7],"B":[-36,0,37],"pairs":[[6,-36],[7,0]],"semantic_template":"qf-function-range-set/{\"A\":[6,7],\"B\":[-36,0,37],\"operation\":\"range\",\"pairs\":[[6,-36],[7,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0020","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={7, 8, 9}、B={-38, 0, 39}，輸入輸出有序對為 [(7, 0), (8, 39), (9, -38)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-38, 0, 39}","explanation_zh":"值域為 {-38, 0, 39}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303220,"parameters":{"operation":"range","A":[7,8,9],"B":[-38,0,39],"pairs":[[7,0],[8,39],[9,-38]],"semantic_template":"qf-function-range-set/{\"A\":[7,8,9],\"B\":[-38,0,39],\"operation\":\"range\",\"pairs\":[[7,0],[8,39],[9,-38]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0021","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={8, 9, 10, 11}、B={-40, 0, 41}，輸入輸出有序對為 [(8, 41), (9, -40), (10, 0), (11, 41)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-40, 0, 41}","explanation_zh":"值域為 {-40, 0, 41}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303221,"parameters":{"operation":"range","A":[8,9,10,11],"B":[-40,0,41],"pairs":[[8,41],[9,-40],[10,0],[11,41]],"semantic_template":"qf-function-range-set/{\"A\":[8,9,10,11],\"B\":[-40,0,41],\"operation\":\"range\",\"pairs\":[[8,41],[9,-40],[10,0],[11,41]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0022","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={9, 10}、B={-42, 0, 43}，輸入輸出有序對為 [(9, -42), (10, 0)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-42, 0}","explanation_zh":"值域為 {-42, 0}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303222,"parameters":{"operation":"range","A":[9,10],"B":[-42,0,43],"pairs":[[9,-42],[10,0]],"semantic_template":"qf-function-range-set/{\"A\":[9,10],\"B\":[-42,0,43],\"operation\":\"range\",\"pairs\":[[9,-42],[10,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0023","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={10, 11, 12}、B={-44, 0, 45}，輸入輸出有序對為 [(10, 0), (11, 45), (12, -44)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-44, 0, 45}","explanation_zh":"值域為 {-44, 0, 45}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303223,"parameters":{"operation":"range","A":[10,11,12],"B":[-44,0,45],"pairs":[[10,0],[11,45],[12,-44]],"semantic_template":"qf-function-range-set/{\"A\":[10,11,12],\"B\":[-44,0,45],\"operation\":\"range\",\"pairs\":[[10,0],[11,45],[12,-44]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0024","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={11, 12, 13, 14}、B={-46, 0, 47}，輸入輸出有序對為 [(11, 47), (12, -46), (13, 0), (14, 47)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-46, 0, 47}","explanation_zh":"值域為 {-46, 0, 47}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303224,"parameters":{"operation":"range","A":[11,12,13,14],"B":[-46,0,47],"pairs":[[11,47],[12,-46],[13,0],[14,47]],"semantic_template":"qf-function-range-set/{\"A\":[11,12,13,14],\"B\":[-46,0,47],\"operation\":\"range\",\"pairs\":[[11,47],[12,-46],[13,0],[14,47]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-range-set-0025","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"讀出函數值域","stem_zh":"明示 A={12, 13}、B={-48, 0, 49}，輸入輸出有序對為 [(12, -48), (13, 0)]。已知它是總函數 f:A→B，請列出值域，集合按數值遞增排列。","answer":{"kind":"short_text","value":"{-48, 0}","explanation_zh":"值域為 {-48, 0}；收集實際輸出並移除重複值，不把陪域中未取到的元素加入。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["像集合","重複輸出去重"]},"variant":{"family_id":"qf-function-range-set","seed":202609303225,"parameters":{"operation":"range","A":[12,13],"B":[-48,0,49],"pairs":[[12,-48],[13,0]],"semantic_template":"qf-function-range-set/{\"A\":[12,13],\"B\":[-48,0,49],\"operation\":\"range\",\"pairs\":[[12,-48],[13,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0001","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A=∅、B=∅，輸入輸出有序對為 []。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"每個 A 中輸入恰有一個 B 中輸出，且沒有額外輸入；故答案為是。空定義域亦按此條件檢查。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303301,"parameters":{"operation":"validity","A":[],"B":[],"pairs":[],"semantic_template":"qf-function-table-validity/{\"A\":[],\"B\":[],\"operation\":\"validity\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0002","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={0}、B=∅，輸入輸出有序對為 []。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 0 沒有輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303302,"parameters":{"operation":"validity","A":[0],"B":[],"pairs":[],"semantic_template":"qf-function-table-validity/{\"A\":[0],\"B\":[],\"operation\":\"validity\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0003","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={0}、B=∅，輸入輸出有序對為 [(0, 0)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸出 0 不在 B，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303303,"parameters":{"operation":"validity","A":[0],"B":[],"pairs":[[0,0]],"semantic_template":"qf-function-table-validity/{\"A\":[0],\"B\":[],\"operation\":\"validity\",\"pairs\":[[0,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0004","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={-9, -8}、B={-6, 0, 7}，輸入輸出有序對為 [(-9, -6), (-8, 0), (-9, 0)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 -9 有多個輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303304,"parameters":{"operation":"validity","A":[-9,-8],"B":[-6,0,7],"pairs":[[-9,-6],[-8,0],[-9,0]],"semantic_template":"qf-function-table-validity/{\"A\":[-9,-8],\"B\":[-6,0,7],\"operation\":\"validity\",\"pairs\":[[-9,-6],[-9,0],[-8,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0005","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={-8, -7, -6}、B={-8, 0, 9}，輸入輸出有序對為 [(-8, 0), (-7, 9), (-6, -8), (-5, -8)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 -5 不在 A，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303305,"parameters":{"operation":"validity","A":[-8,-7,-6],"B":[-8,0,9],"pairs":[[-8,0],[-7,9],[-6,-8],[-5,-8]],"semantic_template":"qf-function-table-validity/{\"A\":[-8,-7,-6],\"B\":[-8,0,9],\"operation\":\"validity\",\"pairs\":[[-8,0],[-7,9],[-6,-8],[-5,-8]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0006","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={-7, -6, -5, -4}、B={-10, 0, 11}，輸入輸出有序對為 [(-7, 11), (-6, -10), (-5, 0), (-4, 11)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"每個 A 中輸入恰有一個 B 中輸出，且沒有額外輸入；故答案為是。空定義域亦按此條件檢查。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303306,"parameters":{"operation":"validity","A":[-7,-6,-5,-4],"B":[-10,0,11],"pairs":[[-7,11],[-6,-10],[-5,0],[-4,11]],"semantic_template":"qf-function-table-validity/{\"A\":[-7,-6,-5,-4],\"B\":[-10,0,11],\"operation\":\"validity\",\"pairs\":[[-7,11],[-6,-10],[-5,0],[-4,11]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0007","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={-6, -5}、B={-12, 0, 13}，輸入輸出有序對為 [(-5, 0)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 -6 沒有輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303307,"parameters":{"operation":"validity","A":[-6,-5],"B":[-12,0,13],"pairs":[[-5,0]],"semantic_template":"qf-function-table-validity/{\"A\":[-6,-5],\"B\":[-12,0,13],\"operation\":\"validity\",\"pairs\":[[-5,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0008","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={-5, -4, -3}、B={-14, 0, 15}，輸入輸出有序對為 [(-5, 107), (-4, 15), (-3, -14)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸出 107 不在 B，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303308,"parameters":{"operation":"validity","A":[-5,-4,-3],"B":[-14,0,15],"pairs":[[-5,107],[-4,15],[-3,-14]],"semantic_template":"qf-function-table-validity/{\"A\":[-5,-4,-3],\"B\":[-14,0,15],\"operation\":\"validity\",\"pairs\":[[-5,107],[-4,15],[-3,-14]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0009","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={-4, -3, -2, -1}、B={-16, 0, 17}，輸入輸出有序對為 [(-4, 17), (-3, -16), (-2, 0), (-1, 17), (-4, -16)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 -4 有多個輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303309,"parameters":{"operation":"validity","A":[-4,-3,-2,-1],"B":[-16,0,17],"pairs":[[-4,17],[-3,-16],[-2,0],[-1,17],[-4,-16]],"semantic_template":"qf-function-table-validity/{\"A\":[-4,-3,-2,-1],\"B\":[-16,0,17],\"operation\":\"validity\",\"pairs\":[[-4,-16],[-4,17],[-3,-16],[-2,0],[-1,17]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0010","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={-3, -2}、B={-18, 0, 19}，輸入輸出有序對為 [(-3, -18), (-2, 0), (-1, -18)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 -1 不在 A，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303310,"parameters":{"operation":"validity","A":[-3,-2],"B":[-18,0,19],"pairs":[[-3,-18],[-2,0],[-1,-18]],"semantic_template":"qf-function-table-validity/{\"A\":[-3,-2],\"B\":[-18,0,19],\"operation\":\"validity\",\"pairs\":[[-3,-18],[-2,0],[-1,-18]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0011","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={-2, -1, 0}、B={-20, 0, 21}，輸入輸出有序對為 [(-2, 0), (-1, 21), (0, -20)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"每個 A 中輸入恰有一個 B 中輸出，且沒有額外輸入；故答案為是。空定義域亦按此條件檢查。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303311,"parameters":{"operation":"validity","A":[-2,-1,0],"B":[-20,0,21],"pairs":[[-2,0],[-1,21],[0,-20]],"semantic_template":"qf-function-table-validity/{\"A\":[-2,-1,0],\"B\":[-20,0,21],\"operation\":\"validity\",\"pairs\":[[-2,0],[-1,21],[0,-20]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0012","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={-1, 0, 1, 2}、B={-22, 0, 23}，輸入輸出有序對為 [(0, -22), (1, 0), (2, 23)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 -1 沒有輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303312,"parameters":{"operation":"validity","A":[-1,0,1,2],"B":[-22,0,23],"pairs":[[0,-22],[1,0],[2,23]],"semantic_template":"qf-function-table-validity/{\"A\":[-1,0,1,2],\"B\":[-22,0,23],\"operation\":\"validity\",\"pairs\":[[0,-22],[1,0],[2,23]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0013","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={0, 1}、B={-24, 0, 25}，輸入輸出有序對為 [(0, 112), (1, 0)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸出 112 不在 B，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303313,"parameters":{"operation":"validity","A":[0,1],"B":[-24,0,25],"pairs":[[0,112],[1,0]],"semantic_template":"qf-function-table-validity/{\"A\":[0,1],\"B\":[-24,0,25],\"operation\":\"validity\",\"pairs\":[[0,112],[1,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0014","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={1, 2, 3}、B={-26, 0, 27}，輸入輸出有序對為 [(1, 0), (2, 27), (3, -26), (1, 27)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 1 有多個輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303314,"parameters":{"operation":"validity","A":[1,2,3],"B":[-26,0,27],"pairs":[[1,0],[2,27],[3,-26],[1,27]],"semantic_template":"qf-function-table-validity/{\"A\":[1,2,3],\"B\":[-26,0,27],\"operation\":\"validity\",\"pairs\":[[1,0],[1,27],[2,27],[3,-26]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0015","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={2, 3, 4, 5}、B={-28, 0, 29}，輸入輸出有序對為 [(2, 29), (3, -28), (4, 0), (5, 29), (6, -28)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 6 不在 A，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303315,"parameters":{"operation":"validity","A":[2,3,4,5],"B":[-28,0,29],"pairs":[[2,29],[3,-28],[4,0],[5,29],[6,-28]],"semantic_template":"qf-function-table-validity/{\"A\":[2,3,4,5],\"B\":[-28,0,29],\"operation\":\"validity\",\"pairs\":[[2,29],[3,-28],[4,0],[5,29],[6,-28]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0016","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={3, 4}、B={-30, 0, 31}，輸入輸出有序對為 [(3, -30), (4, 0)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"每個 A 中輸入恰有一個 B 中輸出，且沒有額外輸入；故答案為是。空定義域亦按此條件檢查。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303316,"parameters":{"operation":"validity","A":[3,4],"B":[-30,0,31],"pairs":[[3,-30],[4,0]],"semantic_template":"qf-function-table-validity/{\"A\":[3,4],\"B\":[-30,0,31],\"operation\":\"validity\",\"pairs\":[[3,-30],[4,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0017","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={4, 5, 6}、B={-32, 0, 33}，輸入輸出有序對為 [(5, 33), (6, -32)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 4 沒有輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303317,"parameters":{"operation":"validity","A":[4,5,6],"B":[-32,0,33],"pairs":[[5,33],[6,-32]],"semantic_template":"qf-function-table-validity/{\"A\":[4,5,6],\"B\":[-32,0,33],\"operation\":\"validity\",\"pairs\":[[5,33],[6,-32]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0018","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={5, 6, 7, 8}、B={-34, 0, 35}，輸入輸出有序對為 [(5, 117), (6, -34), (7, 0), (8, 35)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸出 117 不在 B，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303318,"parameters":{"operation":"validity","A":[5,6,7,8],"B":[-34,0,35],"pairs":[[5,117],[6,-34],[7,0],[8,35]],"semantic_template":"qf-function-table-validity/{\"A\":[5,6,7,8],\"B\":[-34,0,35],\"operation\":\"validity\",\"pairs\":[[5,117],[6,-34],[7,0],[8,35]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0019","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={6, 7}、B={-36, 0, 37}，輸入輸出有序對為 [(6, -36), (7, 0), (6, 0)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 6 有多個輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303319,"parameters":{"operation":"validity","A":[6,7],"B":[-36,0,37],"pairs":[[6,-36],[7,0],[6,0]],"semantic_template":"qf-function-table-validity/{\"A\":[6,7],\"B\":[-36,0,37],\"operation\":\"validity\",\"pairs\":[[6,-36],[6,0],[7,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0020","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={7, 8, 9}、B={-38, 0, 39}，輸入輸出有序對為 [(7, 0), (8, 39), (9, -38), (10, -38)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 10 不在 A，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303320,"parameters":{"operation":"validity","A":[7,8,9],"B":[-38,0,39],"pairs":[[7,0],[8,39],[9,-38],[10,-38]],"semantic_template":"qf-function-table-validity/{\"A\":[7,8,9],\"B\":[-38,0,39],\"operation\":\"validity\",\"pairs\":[[7,0],[8,39],[9,-38],[10,-38]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0021","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={8, 9, 10, 11}、B={-40, 0, 41}，輸入輸出有序對為 [(8, 41), (9, -40), (10, 0), (11, 41)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"每個 A 中輸入恰有一個 B 中輸出，且沒有額外輸入；故答案為是。空定義域亦按此條件檢查。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303321,"parameters":{"operation":"validity","A":[8,9,10,11],"B":[-40,0,41],"pairs":[[8,41],[9,-40],[10,0],[11,41]],"semantic_template":"qf-function-table-validity/{\"A\":[8,9,10,11],\"B\":[-40,0,41],\"operation\":\"validity\",\"pairs\":[[8,41],[9,-40],[10,0],[11,41]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0022","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={9, 10}、B={-42, 0, 43}，輸入輸出有序對為 [(10, 0)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 9 沒有輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303322,"parameters":{"operation":"validity","A":[9,10],"B":[-42,0,43],"pairs":[[10,0]],"semantic_template":"qf-function-table-validity/{\"A\":[9,10],\"B\":[-42,0,43],\"operation\":\"validity\",\"pairs\":[[10,0]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0023","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={10, 11, 12}、B={-44, 0, 45}，輸入輸出有序對為 [(10, 122), (11, 45), (12, -44)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸出 122 不在 B，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303323,"parameters":{"operation":"validity","A":[10,11,12],"B":[-44,0,45],"pairs":[[10,122],[11,45],[12,-44]],"semantic_template":"qf-function-table-validity/{\"A\":[10,11,12],\"B\":[-44,0,45],\"operation\":\"validity\",\"pairs\":[[10,122],[11,45],[12,-44]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0024","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={11, 12, 13, 14}、B={-46, 0, 47}，輸入輸出有序對為 [(11, 47), (12, -46), (13, 0), (14, 47), (11, -46)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 11 有多個輸出，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303324,"parameters":{"operation":"validity","A":[11,12,13,14],"B":[-46,0,47],"pairs":[[11,47],[12,-46],[13,0],[14,47],[11,-46]],"semantic_template":"qf-function-table-validity/{\"A\":[11,12,13,14],\"B\":[-46,0,47],\"operation\":\"validity\",\"pairs\":[[11,-46],[11,47],[12,-46],[13,0],[14,47]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r03-function-table-validity-0025","batch_id":"batch-20260930-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"有限總函數表檢查","stem_zh":"明示 A={12, 13}、B={-48, 0, 49}，輸入輸出有序對為 [(12, -48), (13, 0), (14, -48)]。這份資料是否完整定義總函數 f:A→B？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"因為輸入 14 不在 A，所以答案為否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["總函數條件","集合邊界"]},"variant":{"family_id":"qf-function-table-validity","seed":202609303325,"parameters":{"operation":"validity","A":[12,13],"B":[-48,0,49],"pairs":[[12,-48],[13,0],[14,-48]],"semantic_template":"qf-function-table-validity/{\"A\":[12,13],\"B\":[-48,0,49],\"operation\":\"validity\",\"pairs\":[[12,-48],[13,0],[14,-48]]}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}