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{"schema_version":"ocme-question-v0.1","id":"q-20260913-natural-number-membership-0020","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-natural-number"],"title_zh":"自然數隸屬判定","stem_zh":"依 OCME 本條目「N 包含 0」的慣例，-3.75 是否屬於 N？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-3.75 不符合本條目所用 N 的非負整數範圍；此判定只採 OCME 的包含 0 慣例。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["自然數慣例","集合隸屬"]},"variant":{"family_id":"qf-natural-number-membership","seed":20260932,"parameters":{"value":-3.75,"scenario":"non_integer","semantic_template":"natural/non_integer/value--3.75"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0001","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={1、2} 為明示列舉的有限集合。2 是否滿足 2∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"2 出現在 A 的明示列舉中，因此 2∈A。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260933,"parameters":{"elements":[1,2],"query":2,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-1,2/query-2"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0002","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={11、12、13} 為明示列舉的有限集合。18 是否滿足 18∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"18 未出現在 A 的明示列舉中，因此 18∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260934,"parameters":{"elements":[11,12,13],"query":18,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-11,12,13/query-18"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0003","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={21、22、23、24} 為明示列舉的有限集合。24 是否滿足 24∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"24 出現在 A 的明示列舉中，因此 24∈A。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260935,"parameters":{"elements":[21,22,23,24],"query":24,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-21,22,23,24/query-24"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0004","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={31、32} 為明示列舉的有限集合。37 是否滿足 37∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"37 未出現在 A 的明示列舉中，因此 37∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260936,"parameters":{"elements":[31,32],"query":37,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-31,32/query-37"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0005","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={41、42、43} 為明示列舉的有限集合。43 是否滿足 43∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"43 出現在 A 的明示列舉中，因此 43∈A。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260937,"parameters":{"elements":[41,42,43],"query":43,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-41,42,43/query-43"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0006","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={51、52、53、54} 為明示列舉的有限集合。59 是否滿足 59∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"59 未出現在 A 的明示列舉中，因此 59∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260938,"parameters":{"elements":[51,52,53,54],"query":59,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-51,52,53,54/query-59"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0007","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={61、62} 為明示列舉的有限集合。62 是否滿足 62∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"62 出現在 A 的明示列舉中，因此 62∈A。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260939,"parameters":{"elements":[61,62],"query":62,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-61,62/query-62"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0008","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={71、72、73} 為明示列舉的有限集合。78 是否滿足 78∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"78 未出現在 A 的明示列舉中，因此 78∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260940,"parameters":{"elements":[71,72,73],"query":78,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-71,72,73/query-78"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0009","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={81、82、83、84} 為明示列舉的有限集合。82 是否滿足 82∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"82 出現在 A 的明示列舉中，因此 82∈A。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260941,"parameters":{"elements":[81,82,83,84],"query":82,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-81,82,83,84/query-82"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0010","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={91、92} 為明示列舉的有限集合。97 是否滿足 97∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"97 未出現在 A 的明示列舉中，因此 97∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260942,"parameters":{"elements":[91,92],"query":97,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-91,92/query-97"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0011","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={101、102、103} 為明示列舉的有限集合。103 是否滿足 103∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"103 出現在 A 的明示列舉中，因此 103∈A。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260943,"parameters":{"elements":[101,102,103],"query":103,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-101,102,103/query-103"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0012","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={111、112、113、114} 為明示列舉的有限集合。119 是否滿足 119∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"119 未出現在 A 的明示列舉中，因此 119∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260944,"parameters":{"elements":[111,112,113,114],"query":119,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-111,112,113,114/query-119"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0013","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={121、122} 為明示列舉的有限集合。122 是否滿足 122∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"122 出現在 A 的明示列舉中，因此 122∈A。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260945,"parameters":{"elements":[121,122],"query":122,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-121,122/query-122"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0014","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={131、132、133} 為明示列舉的有限集合。138 是否滿足 138∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"138 未出現在 A 的明示列舉中，因此 138∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260946,"parameters":{"elements":[131,132,133],"query":138,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-131,132,133/query-138"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0015","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={141、142、143、144} 為明示列舉的有限集合。144 是否滿足 144∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"144 出現在 A 的明示列舉中，因此 144∈A。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260947,"parameters":{"elements":[141,142,143,144],"query":144,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-141,142,143,144/query-144"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0016","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={151、152} 為明示列舉的有限集合。157 是否滿足 157∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"157 未出現在 A 的明示列舉中，因此 157∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260948,"parameters":{"elements":[151,152],"query":157,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-151,152/query-157"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0017","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={161、162、163} 為明示列舉的有限集合。163 是否滿足 163∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"163 出現在 A 的明示列舉中，因此 163∈A。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260949,"parameters":{"elements":[161,162,163],"query":163,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-161,162,163/query-163"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0018","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={171、172、173、174} 為明示列舉的有限集合。179 是否滿足 179∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"179 未出現在 A 的明示列舉中，因此 179∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260950,"parameters":{"elements":[171,172,173,174],"query":179,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-171,172,173,174/query-179"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0019","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={181、182} 為明示列舉的有限集合。182 是否滿足 182∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"182 出現在 A 的明示列舉中，因此 182∈A。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260951,"parameters":{"elements":[181,182],"query":182,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-181,182/query-182"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0020","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={191、192、193} 為明示列舉的有限集合。198 是否滿足 198∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"198 未出現在 A 的明示列舉中，因此 198∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260952,"parameters":{"elements":[191,192,193],"query":198,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-191,192,193/query-198"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0021","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={201、202、203、204} 為明示列舉的有限集合。202 是否滿足 202∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"202 出現在 A 的明示列舉中，因此 202∈A。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260953,"parameters":{"elements":[201,202,203,204],"query":202,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-201,202,203,204/query-202"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0022","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={211、212} 為明示列舉的有限集合。217 是否滿足 217∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"217 未出現在 A 的明示列舉中，因此 217∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260954,"parameters":{"elements":[211,212],"query":217,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-211,212/query-217"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0023","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={221、222、223} 為明示列舉的有限集合。223 是否滿足 223∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"223 出現在 A 的明示列舉中，因此 223∈A。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260955,"parameters":{"elements":[221,222,223],"query":223,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-221,222,223/query-223"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0024","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={231、232、233、234} 為明示列舉的有限集合。239 是否滿足 239∈A？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"239 未出現在 A 的明示列舉中，因此 239∉A；本題只判定這個有限列舉。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260956,"parameters":{"elements":[231,232,233,234],"query":239,"scenario":"unlisted_element","semantic_template":"finite-set/unlisted_element/elements-231,232,233,234/query-239"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-set-membership-0025","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-set-membership"],"title_zh":"有限集合隸屬判定","stem_zh":"令 A={241、242} 為明示列舉的有限集合。242 是否滿足 242∈A？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"242 出現在 A 的明示列舉中，因此 242∈A。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合隸屬","有限列舉"]},"variant":{"family_id":"qf-finite-set-membership","seed":20260957,"parameters":{"elements":[241,242],"query":242,"scenario":"listed_element","semantic_template":"finite-set/listed_element/elements-241,242/query-242"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-proposition-classification-0001","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-proposition"],"title_zh":"命題分類","stem_zh":"在本題指定的入門古典邏輯語境中，「0 屬於本條目所用的 N。」 是否為命題？只分類，不判定真偽或證明狀態。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"它是可在指定古典語境談論真假的封閉陳述；是命題不表示它已被證明為真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["命題分類","語句封閉性"]},"variant":{"family_id":"qf-proposition-classification","seed":20260958,"parameters":{"kind":"closed_declarative","form":"membership_constant","text":"「0 屬於本條目所用的 N。」","semantic_template":"proposition/closed_declarative/membership_constant"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-proposition-classification-0002","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-proposition"],"title_zh":"命題分類","stem_zh":"在本題指定的入門古典邏輯語境中，「7=7。」 是否為命題？只分類，不判定真偽或證明狀態。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"它是可在指定古典語境談論真假的封閉陳述；是命題不表示它已被證明為真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["命題分類","語句封閉性"]},"variant":{"family_id":"qf-proposition-classification","seed":20260959,"parameters":{"kind":"closed_declarative","form":"numeric_identity","text":"「7=7。」","semantic_template":"proposition/closed_declarative/numeric_identity"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-proposition-classification-0003","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-proposition"],"title_zh":"命題分類","stem_zh":"在本題指定的入門古典邏輯語境中，「3 大於 9。」 是否為命題？只分類，不判定真偽或證明狀態。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"它是可在指定古典語境談論真假的封閉陳述；是命題不表示它已被證明為真。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["命題分類","語句封閉性"]},"variant":{"family_id":"qf-proposition-classification","seed":20260960,"parameters":{"kind":"closed_declarative","form":"numeric_inequality","text":"「3 大於 9。」","semantic_template":"proposition/closed_declarative/numeric_inequality"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-proposition-classification-0004","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-proposition"],"title_zh":"命題分類","stem_zh":"在本題指定的入門古典邏輯語境中，「0=1。」 是否為命題？只分類，不判定真偽或證明狀態。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"它是可在指定古典語境談論真假的封閉陳述；是命題不表示它已被證明為真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["命題分類","語句封閉性"]},"variant":{"family_id":"qf-proposition-classification","seed":20260961,"parameters":{"kind":"closed_declarative","form":"numeric_distinctness","text":"「0=1。」","semantic_template":"proposition/closed_declarative/numeric_distinctness"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-proposition-classification-0005","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-proposition"],"title_zh":"命題分類","stem_zh":"在本題指定的入門古典邏輯語境中，「5 小於 8。」 是否為命題？只分類，不判定真偽或證明狀態。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"它是可在指定古典語境談論真假的封閉陳述；是命題不表示它已被證明為真。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["命題分類","語句封閉性"]},"variant":{"family_id":"qf-proposition-classification","seed":20260962,"parameters":{"kind":"closed_declarative","form":"numeric_less_than","text":"「5 小於 8。」","semantic_template":"proposition/closed_declarative/numeric_less_than"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20260913-proposition-classification-0023","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-proposition"],"title_zh":"命題分類","stem_zh":"在本題指定的入門古典邏輯語境中，「P 已被證明了嗎？」 是否為命題？只分類，不判定真偽或證明狀態。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"它是疑問句，不是可直接斷言或否定的封閉陳述。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["命題分類","語句封閉性"]},"variant":{"family_id":"qf-proposition-classification","seed":20260980,"parameters":{"kind":"question","form":"provability_interrogative","text":"「P 已被證明了嗎？」","semantic_template":"proposition/question/provability_interrogative"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-proposition-classification-0024","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-proposition"],"title_zh":"命題分類","stem_zh":"在本題指定的入門古典邏輯語境中，「不要把 P 當成已證明。」 是否為命題？只分類，不判定真偽或證明狀態。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"它是命令句，不是可直接斷言或否定的封閉陳述。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["命題分類","語句封閉性"]},"variant":{"family_id":"qf-proposition-classification","seed":20260981,"parameters":{"kind":"command","form":"logic_boundary_imperative","text":"「不要把 P 當成已證明。」","semantic_template":"proposition/command/logic_boundary_imperative"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-proposition-classification-0025","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-proposition"],"title_zh":"命題分類","stem_zh":"在本題指定的入門古典邏輯語境中，「存在一個數等於 0。」 是否為命題？只分類，不判定真偽或證明狀態。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"它是可在指定古典語境談論真假的封閉陳述；是命題不表示它已被證明為真。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["命題分類","語句封閉性"]},"variant":{"family_id":"qf-proposition-classification","seed":20260982,"parameters":{"kind":"closed_declarative","form":"existential_identity","text":"「存在一個數等於 0。」","semantic_template":"proposition/closed_declarative/existential_identity"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0007","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x7-1、x7-2、x7-3、x7-4}，陪域 Y={y7-1、y7-2、y7-3、y7-4、y7-5}。有限對應為 x7-1↦y7-1、x7-3↦y7-1、x7-4↦y7-2。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x7-2 沒有指定輸出，不符合定義域中每個輸入都必須有輸出的條件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260989,"parameters":{"domain":["x7-1","x7-2","x7-3","x7-4"],"codomain":["y7-1","y7-2","y7-3","y7-4","y7-5"],"pairs":[["x7-1","y7-1"],["x7-3","y7-1"],["x7-4","y7-2"]],"scenario":"missing_input","semantic_template":"function/missing_input/domain-4/pairs-0>0;2>0;3>1"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0008","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x8-1、x8-2、x8-3、x8-4}，陪域 Y={y8-1、y8-2、y8-3、y8-4、y8-5}。有限對應為 x8-1↦y8-1、x8-2↦z8、x8-3↦y8-1、x8-4↦y8-2。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"輸出 z8 不屬於明示陪域 Y，因此這不是所宣告的 f:X→Y；陪域與實際值域不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260990,"parameters":{"domain":["x8-1","x8-2","x8-3","x8-4"],"codomain":["y8-1","y8-2","y8-3","y8-4","y8-5"],"pairs":[["x8-1","y8-1"],["x8-2","z8"],["x8-3","y8-1"],["x8-4","y8-2"]],"scenario":"outside_codomain","semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>-1;2>0;3>1"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0009","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x9-1、x9-2、x9-3、x9-4}，陪域 Y={y9-1、y9-2、y9-3、y9-4、y9-5}。有限對應為 x9-1↦y9-1、x9-2↦y9-1、x9-3↦y9-2、x9-4↦y9-1。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"X 的每個輸入各有一個輸出，且所有輸出都屬於陪域 Y；實際值域可只是 Y 的子集。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260991,"parameters":{"domain":["x9-1","x9-2","x9-3","x9-4"],"codomain":["y9-1","y9-2","y9-3","y9-4","y9-5"],"pairs":[["x9-1","y9-1"],["x9-2","y9-1"],["x9-3","y9-2"],["x9-4","y9-1"]],"scenario":"valid","semantic_template":"function/valid/domain-4/pairs-0>0;1>0;2>1;3>0"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0010","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x10-1、x10-2、x10-3、x10-4}，陪域 Y={y10-1、y10-2、y10-3、y10-4、y10-5}。有限對應為 x10-1↦y10-1、x10-2↦y10-1、x10-3↦y10-2、x10-4↦y10-1、x10-3↦y10-3。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x10-3 有兩個不同輸出，不符合每個輸入恰有一個輸出的條件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260992,"parameters":{"domain":["x10-1","x10-2","x10-3","x10-4"],"codomain":["y10-1","y10-2","y10-3","y10-4","y10-5"],"pairs":[["x10-1","y10-1"],["x10-2","y10-1"],["x10-3","y10-2"],["x10-4","y10-1"],["x10-3","y10-3"]],"scenario":"multiple_outputs","semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>0;2>1;2>2;3>0"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0011","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x11-1、x11-2、x11-3、x11-4}，陪域 Y={y11-1、y11-2、y11-3、y11-4、y11-5}。有限對應為 x11-1↦y11-1、x11-2↦y11-1、x11-4↦y11-1。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x11-3 沒有指定輸出，不符合定義域中每個輸入都必須有輸出的條件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260993,"parameters":{"domain":["x11-1","x11-2","x11-3","x11-4"],"codomain":["y11-1","y11-2","y11-3","y11-4","y11-5"],"pairs":[["x11-1","y11-1"],["x11-2","y11-1"],["x11-4","y11-1"]],"scenario":"missing_input","semantic_template":"function/missing_input/domain-4/pairs-0>0;1>0;3>0"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0012","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x12-1、x12-2、x12-3、x12-4}，陪域 Y={y12-1、y12-2、y12-3、y12-4、y12-5}。有限對應為 x12-1↦y12-1、x12-2↦y12-1、x12-3↦z12、x12-4↦y12-1。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"輸出 z12 不屬於明示陪域 Y，因此這不是所宣告的 f:X→Y；陪域與實際值域不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260994,"parameters":{"domain":["x12-1","x12-2","x12-3","x12-4"],"codomain":["y12-1","y12-2","y12-3","y12-4","y12-5"],"pairs":[["x12-1","y12-1"],["x12-2","y12-1"],["x12-3","z12"],["x12-4","y12-1"]],"scenario":"outside_codomain","semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>0;2>-1;3>0"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0013","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x13-1、x13-2、x13-3、x13-4}，陪域 Y={y13-1、y13-2、y13-3、y13-4、y13-5}。有限對應為 x13-1↦y13-1、x13-2↦y13-1、x13-3↦y13-2、x13-4↦y13-2。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"X 的每個輸入各有一個輸出，且所有輸出都屬於陪域 Y；實際值域可只是 Y 的子集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260995,"parameters":{"domain":["x13-1","x13-2","x13-3","x13-4"],"codomain":["y13-1","y13-2","y13-3","y13-4","y13-5"],"pairs":[["x13-1","y13-1"],["x13-2","y13-1"],["x13-3","y13-2"],["x13-4","y13-2"]],"scenario":"valid","semantic_template":"function/valid/domain-4/pairs-0>0;1>0;2>1;3>1"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0014","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x14-1、x14-2、x14-3、x14-4}，陪域 Y={y14-1、y14-2、y14-3、y14-4、y14-5}。有限對應為 x14-1↦y14-1、x14-2↦y14-1、x14-3↦y14-2、x14-4↦y14-2、x14-4↦y14-3。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x14-4 有兩個不同輸出，不符合每個輸入恰有一個輸出的條件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260996,"parameters":{"domain":["x14-1","x14-2","x14-3","x14-4"],"codomain":["y14-1","y14-2","y14-3","y14-4","y14-5"],"pairs":[["x14-1","y14-1"],["x14-2","y14-1"],["x14-3","y14-2"],["x14-4","y14-2"],["x14-4","y14-3"]],"scenario":"multiple_outputs","semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>0;2>1;3>1;3>2"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0015","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x15-1、x15-2、x15-3、x15-4}，陪域 Y={y15-1、y15-2、y15-3、y15-4、y15-5}。有限對應為 x15-1↦y15-1、x15-2↦y15-1、x15-3↦y15-2。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x15-4 沒有指定輸出，不符合定義域中每個輸入都必須有輸出的條件。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260997,"parameters":{"domain":["x15-1","x15-2","x15-3","x15-4"],"codomain":["y15-1","y15-2","y15-3","y15-4","y15-5"],"pairs":[["x15-1","y15-1"],["x15-2","y15-1"],["x15-3","y15-2"]],"scenario":"missing_input","semantic_template":"function/missing_input/domain-4/pairs-0>0;1>0;2>1"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0016","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x16-1、x16-2、x16-3、x16-4}，陪域 Y={y16-1、y16-2、y16-3、y16-4、y16-5}。有限對應為 x16-1↦y16-1、x16-2↦y16-1、x16-3↦y16-2、x16-4↦z16。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"輸出 z16 不屬於明示陪域 Y，因此這不是所宣告的 f:X→Y；陪域與實際值域不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260998,"parameters":{"domain":["x16-1","x16-2","x16-3","x16-4"],"codomain":["y16-1","y16-2","y16-3","y16-4","y16-5"],"pairs":[["x16-1","y16-1"],["x16-2","y16-1"],["x16-3","y16-2"],["x16-4","z16"]],"scenario":"outside_codomain","semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>0;2>1;3>-1"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0017","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x17-1、x17-2、x17-3、x17-4}，陪域 Y={y17-1、y17-2、y17-3、y17-4、y17-5}。有限對應為 x17-1↦y17-1、x17-2↦y17-1、x17-3↦y17-2、x17-4↦y17-3。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"X 的每個輸入各有一個輸出，且所有輸出都屬於陪域 Y；實際值域可只是 Y 的子集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20260999,"parameters":{"domain":["x17-1","x17-2","x17-3","x17-4"],"codomain":["y17-1","y17-2","y17-3","y17-4","y17-5"],"pairs":[["x17-1","y17-1"],["x17-2","y17-1"],["x17-3","y17-2"],["x17-4","y17-3"]],"scenario":"valid","semantic_template":"function/valid/domain-4/pairs-0>0;1>0;2>1;3>2"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0018","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x18-1、x18-2、x18-3、x18-4}，陪域 Y={y18-1、y18-2、y18-3、y18-4、y18-5}。有限對應為 x18-1↦y18-1、x18-2↦y18-1、x18-3↦y18-2、x18-4↦y18-3、x18-1↦y18-2。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x18-1 有兩個不同輸出，不符合每個輸入恰有一個輸出的條件。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261000,"parameters":{"domain":["x18-1","x18-2","x18-3","x18-4"],"codomain":["y18-1","y18-2","y18-3","y18-4","y18-5"],"pairs":[["x18-1","y18-1"],["x18-2","y18-1"],["x18-3","y18-2"],["x18-4","y18-3"],["x18-1","y18-2"]],"scenario":"multiple_outputs","semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;0>1;1>0;2>1;3>2"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0019","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x19-1、x19-2、x19-3、x19-4}，陪域 Y={y19-1、y19-2、y19-3、y19-4、y19-5}。有限對應為 x19-2↦y19-1、x19-3↦y19-2、x19-4↦y19-3。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x19-1 沒有指定輸出，不符合定義域中每個輸入都必須有輸出的條件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261001,"parameters":{"domain":["x19-1","x19-2","x19-3","x19-4"],"codomain":["y19-1","y19-2","y19-3","y19-4","y19-5"],"pairs":[["x19-2","y19-1"],["x19-3","y19-2"],["x19-4","y19-3"]],"scenario":"missing_input","semantic_template":"function/missing_input/domain-4/pairs-1>0;2>1;3>2"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0020","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x20-1、x20-2、x20-3、x20-4}，陪域 Y={y20-1、y20-2、y20-3、y20-4、y20-5}。有限對應為 x20-1↦z20、x20-2↦y20-1、x20-3↦y20-2、x20-4↦y20-3。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"輸出 z20 不屬於明示陪域 Y，因此這不是所宣告的 f:X→Y；陪域與實際值域不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261002,"parameters":{"domain":["x20-1","x20-2","x20-3","x20-4"],"codomain":["y20-1","y20-2","y20-3","y20-4","y20-5"],"pairs":[["x20-1","z20"],["x20-2","y20-1"],["x20-3","y20-2"],["x20-4","y20-3"]],"scenario":"outside_codomain","semantic_template":"function/outside_codomain/domain-4/pairs-0>-1;1>0;2>1;3>2"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0021","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x21-1、x21-2、x21-3、x21-4}，陪域 Y={y21-1、y21-2、y21-3、y21-4、y21-5}。有限對應為 x21-1↦y21-1、x21-2↦y21-2、x21-3↦y21-1、x21-4↦y21-1。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"X 的每個輸入各有一個輸出，且所有輸出都屬於陪域 Y；實際值域可只是 Y 的子集。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261003,"parameters":{"domain":["x21-1","x21-2","x21-3","x21-4"],"codomain":["y21-1","y21-2","y21-3","y21-4","y21-5"],"pairs":[["x21-1","y21-1"],["x21-2","y21-2"],["x21-3","y21-1"],["x21-4","y21-1"]],"scenario":"valid","semantic_template":"function/valid/domain-4/pairs-0>0;1>1;2>0;3>0"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0022","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x22-1、x22-2、x22-3、x22-4}，陪域 Y={y22-1、y22-2、y22-3、y22-4、y22-5}。有限對應為 x22-1↦y22-1、x22-2↦y22-2、x22-3↦y22-1、x22-4↦y22-1、x22-2↦y22-3。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x22-2 有兩個不同輸出，不符合每個輸入恰有一個輸出的條件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261004,"parameters":{"domain":["x22-1","x22-2","x22-3","x22-4"],"codomain":["y22-1","y22-2","y22-3","y22-4","y22-5"],"pairs":[["x22-1","y22-1"],["x22-2","y22-2"],["x22-3","y22-1"],["x22-4","y22-1"],["x22-2","y22-3"]],"scenario":"multiple_outputs","semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>1;1>2;2>0;3>0"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0023","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x23-1、x23-2、x23-3、x23-4}，陪域 Y={y23-1、y23-2、y23-3、y23-4、y23-5}。有限對應為 x23-1↦y23-1、x23-3↦y23-1、x23-4↦y23-1。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x23-2 沒有指定輸出，不符合定義域中每個輸入都必須有輸出的條件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261005,"parameters":{"domain":["x23-1","x23-2","x23-3","x23-4"],"codomain":["y23-1","y23-2","y23-3","y23-4","y23-5"],"pairs":[["x23-1","y23-1"],["x23-3","y23-1"],["x23-4","y23-1"]],"scenario":"missing_input","semantic_template":"function/missing_input/domain-4/pairs-0>0;2>0;3>0"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0024","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x24-1、x24-2、x24-3、x24-4}，陪域 Y={y24-1、y24-2、y24-3、y24-4、y24-5}。有限對應為 x24-1↦y24-1、x24-2↦z24、x24-3↦y24-1、x24-4↦y24-1。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"輸出 z24 不屬於明示陪域 Y，因此這不是所宣告的 f:X→Y；陪域與實際值域不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261006,"parameters":{"domain":["x24-1","x24-2","x24-3","x24-4"],"codomain":["y24-1","y24-2","y24-3","y24-4","y24-5"],"pairs":[["x24-1","y24-1"],["x24-2","z24"],["x24-3","y24-1"],["x24-4","y24-1"]],"scenario":"outside_codomain","semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>-1;2>0;3>0"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0025","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x25-1、x25-2、x25-3、x25-4}，陪域 Y={y25-1、y25-2、y25-3、y25-4、y25-5}。有限對應為 x25-1↦y25-1、x25-2↦y25-2、x25-3↦y25-1、x25-4↦y25-2。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"X 的每個輸入各有一個輸出，且所有輸出都屬於陪域 Y；實際值域可只是 Y 的子集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261007,"parameters":{"domain":["x25-1","x25-2","x25-3","x25-4"],"codomain":["y25-1","y25-2","y25-3","y25-4","y25-5"],"pairs":[["x25-1","y25-1"],["x25-2","y25-2"],["x25-3","y25-1"],["x25-4","y25-2"]],"scenario":"valid","semantic_template":"function/valid/domain-4/pairs-0>0;1>1;2>0;3>1"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0026","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x26-1、x26-2、x26-3、x26-4}，陪域 Y={y26-1、y26-2、y26-3、y26-4、y26-5}。有限對應為 x26-1↦y26-1、x26-2↦y26-2、x26-3↦y26-1、x26-4↦y26-2、x26-3↦y26-2。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x26-3 有兩個不同輸出，不符合每個輸入恰有一個輸出的條件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261008,"parameters":{"domain":["x26-1","x26-2","x26-3","x26-4"],"codomain":["y26-1","y26-2","y26-3","y26-4","y26-5"],"pairs":[["x26-1","y26-1"],["x26-2","y26-2"],["x26-3","y26-1"],["x26-4","y26-2"],["x26-3","y26-2"]],"scenario":"multiple_outputs","semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>1;2>0;2>1;3>1"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0027","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x27-1、x27-2、x27-3、x27-4}，陪域 Y={y27-1、y27-2、y27-3、y27-4、y27-5}。有限對應為 x27-1↦y27-1、x27-2↦y27-2、x27-4↦y27-2。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x27-3 沒有指定輸出，不符合定義域中每個輸入都必須有輸出的條件。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261009,"parameters":{"domain":["x27-1","x27-2","x27-3","x27-4"],"codomain":["y27-1","y27-2","y27-3","y27-4","y27-5"],"pairs":[["x27-1","y27-1"],["x27-2","y27-2"],["x27-4","y27-2"]],"scenario":"missing_input","semantic_template":"function/missing_input/domain-4/pairs-0>0;1>1;3>1"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0028","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x28-1、x28-2、x28-3、x28-4}，陪域 Y={y28-1、y28-2、y28-3、y28-4、y28-5}。有限對應為 x28-1↦y28-1、x28-2↦y28-2、x28-3↦z28、x28-4↦y28-2。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"輸出 z28 不屬於明示陪域 Y，因此這不是所宣告的 f:X→Y；陪域與實際值域不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261010,"parameters":{"domain":["x28-1","x28-2","x28-3","x28-4"],"codomain":["y28-1","y28-2","y28-3","y28-4","y28-5"],"pairs":[["x28-1","y28-1"],["x28-2","y28-2"],["x28-3","z28"],["x28-4","y28-2"]],"scenario":"outside_codomain","semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>1;2>-1;3>1"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0029","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x29-1、x29-2、x29-3、x29-4}，陪域 Y={y29-1、y29-2、y29-3、y29-4、y29-5}。有限對應為 x29-1↦y29-1、x29-2↦y29-2、x29-3↦y29-1、x29-4↦y29-3。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"X 的每個輸入各有一個輸出，且所有輸出都屬於陪域 Y；實際值域可只是 Y 的子集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261011,"parameters":{"domain":["x29-1","x29-2","x29-3","x29-4"],"codomain":["y29-1","y29-2","y29-3","y29-4","y29-5"],"pairs":[["x29-1","y29-1"],["x29-2","y29-2"],["x29-3","y29-1"],["x29-4","y29-3"]],"scenario":"valid","semantic_template":"function/valid/domain-4/pairs-0>0;1>1;2>0;3>2"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260913-finite-function-mapping-0030","batch_id":"batch-20260913-foundational-language","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"有限映射函數判定","stem_zh":"令定義域 X={x30-1、x30-2、x30-3、x30-4}，陪域 Y={y30-1、y30-2、y30-3、y30-4、y30-5}。有限對應為 x30-1↦y30-1、x30-2↦y30-2、x30-3↦y30-1、x30-4↦y30-3、x30-4↦y30-4。它是否定義函數 f:X→Y？請把陪域 Y 與實際值域分開。","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"x30-4 有兩個不同輸出，不符合每個輸入恰有一個輸出的條件。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數定義","定義域與陪域"]},"variant":{"family_id":"qf-finite-function-mapping","seed":20261012,"parameters":{"domain":["x30-1","x30-2","x30-3","x30-4"],"codomain":["y30-1","y30-2","y30-3","y30-4","y30-5"],"pairs":[["x30-1","y30-1"],["x30-2","y30-2"],["x30-3","y30-1"],["x30-4","y30-3"],["x30-4","y30-4"]],"scenario":"multiple_outputs","semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>1;2>0;3>2;3>3"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-13","contract_version":"ocme-question-factory-v0.1"}}