{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0001","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={1, 2, 3}，本題明示 F=P(S)。E={2, 9} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 9 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260919,"parameters":{"S":[1,2,3],"E":[2,9],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[2,9],\"F\":\"P(S)\",\"S\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0002","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={5, 6, 7}，本題明示 F=P(S)。E={5, 7} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260920,"parameters":{"S":[5,6,7],"E":[5,7],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[5,7],\"F\":\"P(S)\",\"S\":[5,6,7]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0003","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={9, 10, 11}，本題明示 F=P(S)。E={10, 17} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 17 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260921,"parameters":{"S":[9,10,11],"E":[10,17],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[10,17],\"F\":\"P(S)\",\"S\":[9,10,11]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0004","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={13, 14, 15}，本題明示 F=P(S)。E={13, 15} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260922,"parameters":{"S":[13,14,15],"E":[13,15],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[13,15],\"F\":\"P(S)\",\"S\":[13,14,15]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0005","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={17, 18, 19}，本題明示 F=P(S)。E={18, 25} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 25 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260923,"parameters":{"S":[17,18,19],"E":[18,25],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[18,25],\"F\":\"P(S)\",\"S\":[17,18,19]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0006","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={21, 22, 23}，本題明示 F=P(S)。E={21, 23} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260924,"parameters":{"S":[21,22,23],"E":[21,23],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[21,23],\"F\":\"P(S)\",\"S\":[21,22,23]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0007","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={25, 26, 27}，本題明示 F=P(S)。E={26, 33} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 33 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260925,"parameters":{"S":[25,26,27],"E":[26,33],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[26,33],\"F\":\"P(S)\",\"S\":[25,26,27]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0008","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={29, 30, 31}，本題明示 F=P(S)。E={29, 31} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260926,"parameters":{"S":[29,30,31],"E":[29,31],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[29,31],\"F\":\"P(S)\",\"S\":[29,30,31]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0009","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={33, 34, 35}，本題明示 F=P(S)。E={34, 41} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 41 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260927,"parameters":{"S":[33,34,35],"E":[34,41],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[34,41],\"F\":\"P(S)\",\"S\":[33,34,35]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0010","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={37, 38, 39}，本題明示 F=P(S)。E={37, 39} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260928,"parameters":{"S":[37,38,39],"E":[37,39],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[37,39],\"F\":\"P(S)\",\"S\":[37,38,39]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0011","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={41, 42, 43}，本題明示 F=P(S)。E={42, 49} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 49 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260929,"parameters":{"S":[41,42,43],"E":[42,49],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[42,49],\"F\":\"P(S)\",\"S\":[41,42,43]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0012","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={45, 46, 47}，本題明示 F=P(S)。E={45, 47} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260930,"parameters":{"S":[45,46,47],"E":[45,47],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[45,47],\"F\":\"P(S)\",\"S\":[45,46,47]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0013","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={49, 50, 51}，本題明示 F=P(S)。E={50, 57} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 57 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260931,"parameters":{"S":[49,50,51],"E":[50,57],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[50,57],\"F\":\"P(S)\",\"S\":[49,50,51]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0014","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={53, 54, 55}，本題明示 F=P(S)。E={53, 55} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260932,"parameters":{"S":[53,54,55],"E":[53,55],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[53,55],\"F\":\"P(S)\",\"S\":[53,54,55]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0015","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={57, 58, 59}，本題明示 F=P(S)。E={58, 65} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 65 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260933,"parameters":{"S":[57,58,59],"E":[58,65],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[58,65],\"F\":\"P(S)\",\"S\":[57,58,59]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0016","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={61, 62, 63}，本題明示 F=P(S)。E={61, 63} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260934,"parameters":{"S":[61,62,63],"E":[61,63],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[61,63],\"F\":\"P(S)\",\"S\":[61,62,63]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0017","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={65, 66, 67}，本題明示 F=P(S)。E={66, 73} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 73 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260935,"parameters":{"S":[65,66,67],"E":[66,73],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[66,73],\"F\":\"P(S)\",\"S\":[65,66,67]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0018","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={69, 70, 71}，本題明示 F=P(S)。E={69, 71} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260936,"parameters":{"S":[69,70,71],"E":[69,71],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[69,71],\"F\":\"P(S)\",\"S\":[69,70,71]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0019","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={73, 74, 75}，本題明示 F=P(S)。E={74, 81} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 81 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260937,"parameters":{"S":[73,74,75],"E":[74,81],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[74,81],\"F\":\"P(S)\",\"S\":[73,74,75]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0020","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={77, 78, 79}，本題明示 F=P(S)。E={77, 79} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260938,"parameters":{"S":[77,78,79],"E":[77,79],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[77,79],\"F\":\"P(S)\",\"S\":[77,78,79]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0021","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={81, 82, 83}，本題明示 F=P(S)。E={82, 89} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 89 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260939,"parameters":{"S":[81,82,83],"E":[82,89],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[82,89],\"F\":\"P(S)\",\"S\":[81,82,83]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0022","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={85, 86, 87}，本題明示 F=P(S)。E={85, 87} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260940,"parameters":{"S":[85,86,87],"E":[85,87],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[85,87],\"F\":\"P(S)\",\"S\":[85,86,87]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0023","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={89, 90, 91}，本題明示 F=P(S)。E={90, 97} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 97 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260941,"parameters":{"S":[89,90,91],"E":[90,97],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[90,97],\"F\":\"P(S)\",\"S\":[89,90,91]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0024","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={93, 94, 95}，本題明示 F=P(S)。E={93, 95} 是否為本模型的事件？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"E⊆S 且 F=P(S)，所以 E 是事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260942,"parameters":{"S":[93,94,95],"E":[93,95],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[93,95],\"F\":\"P(S)\",\"S\":[93,94,95]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-subset-validity-0025","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-subset-validity","stem_zh":"S={97, 98, 99}，本題明示 F=P(S)。E={98, 105} 是否為本模型的事件？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"元素 105 不在 S 中，故 E 不是 S 的子集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件","冪集模型"]},"variant":{"family_id":"qf-finite-event-subset-validity","seed":20260943,"parameters":{"S":[97,98,99],"E":[98,105],"F":"P(S)","semantic_template":"qf-finite-event-subset-validity/{\"E\":[98,105],\"F\":\"P(S)\",\"S\":[97,98,99]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0001","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={1, 2, 3}，F=P(S)。1 是單一結果；{1} 是事件。1 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"1 是 S 的元素；{1} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261019,"parameters":{"S":[1,2,3],"x":1,"E":[1],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[1],\"F\":\"P(S)\",\"S\":[1,2,3],\"x\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0002","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={5, 6, 7}，F=P(S)。6 是單一結果；{6} 是事件。6 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"6 是 S 的元素；{6} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261020,"parameters":{"S":[5,6,7],"x":6,"E":[6],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[6],\"F\":\"P(S)\",\"S\":[5,6,7],\"x\":6}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0003","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={9, 10, 11}，F=P(S)。11 是單一結果；{11} 是事件。11 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"11 是 S 的元素；{11} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261021,"parameters":{"S":[9,10,11],"x":11,"E":[11],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[11],\"F\":\"P(S)\",\"S\":[9,10,11],\"x\":11}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0004","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={13, 14, 15}，F=P(S)。13 是單一結果；{13} 是事件。13 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"13 是 S 的元素；{13} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261022,"parameters":{"S":[13,14,15],"x":13,"E":[13],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[13],\"F\":\"P(S)\",\"S\":[13,14,15],\"x\":13}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0005","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={17, 18, 19}，F=P(S)。18 是單一結果；{18} 是事件。18 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"18 是 S 的元素；{18} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261023,"parameters":{"S":[17,18,19],"x":18,"E":[18],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[18],\"F\":\"P(S)\",\"S\":[17,18,19],\"x\":18}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0006","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={21, 22, 23}，F=P(S)。23 是單一結果；{23} 是事件。23 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"23 是 S 的元素；{23} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261024,"parameters":{"S":[21,22,23],"x":23,"E":[23],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[23],\"F\":\"P(S)\",\"S\":[21,22,23],\"x\":23}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0007","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={25, 26, 27}，F=P(S)。25 是單一結果；{25} 是事件。25 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"25 是 S 的元素；{25} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261025,"parameters":{"S":[25,26,27],"x":25,"E":[25],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[25],\"F\":\"P(S)\",\"S\":[25,26,27],\"x\":25}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0008","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={29, 30, 31}，F=P(S)。30 是單一結果；{30} 是事件。30 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"30 是 S 的元素；{30} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261026,"parameters":{"S":[29,30,31],"x":30,"E":[30],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[30],\"F\":\"P(S)\",\"S\":[29,30,31],\"x\":30}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0009","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={33, 34, 35}，F=P(S)。35 是單一結果；{35} 是事件。35 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"35 是 S 的元素；{35} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261027,"parameters":{"S":[33,34,35],"x":35,"E":[35],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[35],\"F\":\"P(S)\",\"S\":[33,34,35],\"x\":35}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0010","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={37, 38, 39}，F=P(S)。37 是單一結果；{37} 是事件。37 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"37 是 S 的元素；{37} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261028,"parameters":{"S":[37,38,39],"x":37,"E":[37],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[37],\"F\":\"P(S)\",\"S\":[37,38,39],\"x\":37}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0011","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={41, 42, 43}，F=P(S)。42 是單一結果；{42} 是事件。42 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"42 是 S 的元素；{42} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261029,"parameters":{"S":[41,42,43],"x":42,"E":[42],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[42],\"F\":\"P(S)\",\"S\":[41,42,43],\"x\":42}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0012","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={45, 46, 47}，F=P(S)。47 是單一結果；{47} 是事件。47 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"47 是 S 的元素；{47} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261030,"parameters":{"S":[45,46,47],"x":47,"E":[47],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[47],\"F\":\"P(S)\",\"S\":[45,46,47],\"x\":47}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0013","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={49, 50, 51}，F=P(S)。49 是單一結果；{49} 是事件。49 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"49 是 S 的元素；{49} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261031,"parameters":{"S":[49,50,51],"x":49,"E":[49],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[49],\"F\":\"P(S)\",\"S\":[49,50,51],\"x\":49}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0014","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={53, 54, 55}，F=P(S)。54 是單一結果；{54} 是事件。54 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"54 是 S 的元素；{54} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261032,"parameters":{"S":[53,54,55],"x":54,"E":[54],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[54],\"F\":\"P(S)\",\"S\":[53,54,55],\"x\":54}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0015","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={57, 58, 59}，F=P(S)。59 是單一結果；{59} 是事件。59 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"59 是 S 的元素；{59} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261033,"parameters":{"S":[57,58,59],"x":59,"E":[59],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[59],\"F\":\"P(S)\",\"S\":[57,58,59],\"x\":59}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0016","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={61, 62, 63}，F=P(S)。61 是單一結果；{61} 是事件。61 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"61 是 S 的元素；{61} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261034,"parameters":{"S":[61,62,63],"x":61,"E":[61],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[61],\"F\":\"P(S)\",\"S\":[61,62,63],\"x\":61}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0017","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={65, 66, 67}，F=P(S)。66 是單一結果；{66} 是事件。66 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"66 是 S 的元素；{66} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261035,"parameters":{"S":[65,66,67],"x":66,"E":[66],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[66],\"F\":\"P(S)\",\"S\":[65,66,67],\"x\":66}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0018","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={69, 70, 71}，F=P(S)。71 是單一結果；{71} 是事件。71 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"71 是 S 的元素；{71} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261036,"parameters":{"S":[69,70,71],"x":71,"E":[71],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[71],\"F\":\"P(S)\",\"S\":[69,70,71],\"x\":71}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0019","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={73, 74, 75}，F=P(S)。73 是單一結果；{73} 是事件。73 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"73 是 S 的元素；{73} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261037,"parameters":{"S":[73,74,75],"x":73,"E":[73],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[73],\"F\":\"P(S)\",\"S\":[73,74,75],\"x\":73}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0020","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={77, 78, 79}，F=P(S)。78 是單一結果；{78} 是事件。78 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"78 是 S 的元素；{78} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261038,"parameters":{"S":[77,78,79],"x":78,"E":[78],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[78],\"F\":\"P(S)\",\"S\":[77,78,79],\"x\":78}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0021","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={81, 82, 83}，F=P(S)。83 是單一結果；{83} 是事件。83 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"83 是 S 的元素；{83} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261039,"parameters":{"S":[81,82,83],"x":83,"E":[83],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[83],\"F\":\"P(S)\",\"S\":[81,82,83],\"x\":83}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0022","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={85, 86, 87}，F=P(S)。85 是單一結果；{85} 是事件。85 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"85 是 S 的元素；{85} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261040,"parameters":{"S":[85,86,87],"x":85,"E":[85],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[85],\"F\":\"P(S)\",\"S\":[85,86,87],\"x\":85}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0023","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={89, 90, 91}，F=P(S)。90 是單一結果；{90} 是事件。90 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"90 是 S 的元素；{90} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261041,"parameters":{"S":[89,90,91],"x":90,"E":[90],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[90],\"F\":\"P(S)\",\"S\":[89,90,91],\"x\":90}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0024","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={93, 94, 95}，F=P(S)。95 是單一結果；{95} 是事件。95 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"95 是 S 的元素；{95} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261042,"parameters":{"S":[93,94,95],"x":95,"E":[95],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[95],\"F\":\"P(S)\",\"S\":[93,94,95],\"x\":95}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-outcome-versus-event-role-0025","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-outcome-versus-event-role","stem_zh":"S={97, 98, 99}，F=P(S)。97 是單一結果；{97} 是事件。97 的角色是否為「事件集合」？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"97 是 S 的元素；{97} 才是結果集合形式的事件。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["結果與事件"]},"variant":{"family_id":"qf-outcome-versus-event-role","seed":20261043,"parameters":{"S":[97,98,99],"x":97,"E":[97],"F":"P(S)","semantic_template":"qf-outcome-versus-event-role/{\"E\":[97],\"F\":\"P(S)\",\"S\":[97,98,99],\"x\":97}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0001","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={1, 2, 3}，F=P(S)，E={2}。實際結果為 1。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"1不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261119,"parameters":{"S":[1,2,3],"E":[2],"x":1,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[2],\"F\":\"P(S)\",\"S\":[1,2,3],\"x\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0002","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={5, 6, 7}，F=P(S)，E={5, 7}。實際結果為 5。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"5屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261120,"parameters":{"S":[5,6,7],"E":[5,7],"x":5,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[5,7],\"F\":\"P(S)\",\"S\":[5,6,7],\"x\":5}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0003","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={9, 10, 11}，F=P(S)，E={10}。實際結果為 9。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"9不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261121,"parameters":{"S":[9,10,11],"E":[10],"x":9,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[10],\"F\":\"P(S)\",\"S\":[9,10,11],\"x\":9}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0004","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={13, 14, 15}，F=P(S)，E={13, 15}。實際結果為 13。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"13屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261122,"parameters":{"S":[13,14,15],"E":[13,15],"x":13,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[13,15],\"F\":\"P(S)\",\"S\":[13,14,15],\"x\":13}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0005","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={17, 18, 19}，F=P(S)，E={18}。實際結果為 17。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"17不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261123,"parameters":{"S":[17,18,19],"E":[18],"x":17,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[18],\"F\":\"P(S)\",\"S\":[17,18,19],\"x\":17}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0006","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={21, 22, 23}，F=P(S)，E={21, 23}。實際結果為 21。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"21屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261124,"parameters":{"S":[21,22,23],"E":[21,23],"x":21,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[21,23],\"F\":\"P(S)\",\"S\":[21,22,23],\"x\":21}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0007","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={25, 26, 27}，F=P(S)，E={26}。實際結果為 25。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"25不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261125,"parameters":{"S":[25,26,27],"E":[26],"x":25,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[26],\"F\":\"P(S)\",\"S\":[25,26,27],\"x\":25}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0008","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={29, 30, 31}，F=P(S)，E={29, 31}。實際結果為 29。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"29屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261126,"parameters":{"S":[29,30,31],"E":[29,31],"x":29,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[29,31],\"F\":\"P(S)\",\"S\":[29,30,31],\"x\":29}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0009","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={33, 34, 35}，F=P(S)，E={34}。實際結果為 33。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"33不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261127,"parameters":{"S":[33,34,35],"E":[34],"x":33,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[34],\"F\":\"P(S)\",\"S\":[33,34,35],\"x\":33}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0010","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={37, 38, 39}，F=P(S)，E={37, 39}。實際結果為 37。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"37屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261128,"parameters":{"S":[37,38,39],"E":[37,39],"x":37,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[37,39],\"F\":\"P(S)\",\"S\":[37,38,39],\"x\":37}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0011","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={41, 42, 43}，F=P(S)，E={42}。實際結果為 41。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"41不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261129,"parameters":{"S":[41,42,43],"E":[42],"x":41,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[42],\"F\":\"P(S)\",\"S\":[41,42,43],\"x\":41}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0012","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={45, 46, 47}，F=P(S)，E={45, 47}。實際結果為 45。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"45屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261130,"parameters":{"S":[45,46,47],"E":[45,47],"x":45,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[45,47],\"F\":\"P(S)\",\"S\":[45,46,47],\"x\":45}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0013","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={49, 50, 51}，F=P(S)，E={50}。實際結果為 49。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"49不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261131,"parameters":{"S":[49,50,51],"E":[50],"x":49,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[50],\"F\":\"P(S)\",\"S\":[49,50,51],\"x\":49}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0014","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={53, 54, 55}，F=P(S)，E={53, 55}。實際結果為 53。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"53屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261132,"parameters":{"S":[53,54,55],"E":[53,55],"x":53,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[53,55],\"F\":\"P(S)\",\"S\":[53,54,55],\"x\":53}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0015","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={57, 58, 59}，F=P(S)，E={58}。實際結果為 57。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"57不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261133,"parameters":{"S":[57,58,59],"E":[58],"x":57,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[58],\"F\":\"P(S)\",\"S\":[57,58,59],\"x\":57}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0016","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={61, 62, 63}，F=P(S)，E={61, 63}。實際結果為 61。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"61屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261134,"parameters":{"S":[61,62,63],"E":[61,63],"x":61,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[61,63],\"F\":\"P(S)\",\"S\":[61,62,63],\"x\":61}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0017","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={65, 66, 67}，F=P(S)，E={66}。實際結果為 65。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"65不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261135,"parameters":{"S":[65,66,67],"E":[66],"x":65,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[66],\"F\":\"P(S)\",\"S\":[65,66,67],\"x\":65}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0018","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={69, 70, 71}，F=P(S)，E={69, 71}。實際結果為 69。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"69屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261136,"parameters":{"S":[69,70,71],"E":[69,71],"x":69,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[69,71],\"F\":\"P(S)\",\"S\":[69,70,71],\"x\":69}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0019","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={73, 74, 75}，F=P(S)，E={74}。實際結果為 73。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"73不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261137,"parameters":{"S":[73,74,75],"E":[74],"x":73,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[74],\"F\":\"P(S)\",\"S\":[73,74,75],\"x\":73}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0020","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={77, 78, 79}，F=P(S)，E={77, 79}。實際結果為 77。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"77屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261138,"parameters":{"S":[77,78,79],"E":[77,79],"x":77,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[77,79],\"F\":\"P(S)\",\"S\":[77,78,79],\"x\":77}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0021","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={81, 82, 83}，F=P(S)，E={82}。實際結果為 81。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"81不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261139,"parameters":{"S":[81,82,83],"E":[82],"x":81,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[82],\"F\":\"P(S)\",\"S\":[81,82,83],\"x\":81}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0022","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={85, 86, 87}，F=P(S)，E={85, 87}。實際結果為 85。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"85屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261140,"parameters":{"S":[85,86,87],"E":[85,87],"x":85,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[85,87],\"F\":\"P(S)\",\"S\":[85,86,87],\"x\":85}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0023","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={89, 90, 91}，F=P(S)，E={90}。實際結果為 89。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"89不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261141,"parameters":{"S":[89,90,91],"E":[90],"x":89,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[90],\"F\":\"P(S)\",\"S\":[89,90,91],\"x\":89}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0024","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={93, 94, 95}，F=P(S)，E={93, 95}。實際結果為 93。E 是否發生？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"93屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261142,"parameters":{"S":[93,94,95],"E":[93,95],"x":93,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[93,95],\"F\":\"P(S)\",\"S\":[93,94,95],\"x\":93}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-occurrence-0025","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-occurrence","stem_zh":"S={97, 98, 99}，F=P(S)，E={98}。實際結果為 97。E 是否發生？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"97不屬於 E；本題不指派機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件發生"]},"variant":{"family_id":"qf-finite-event-occurrence","seed":20261143,"parameters":{"S":[97,98,99],"E":[98],"x":97,"F":"P(S)","semantic_template":"qf-finite-event-occurrence/{\"E\":[98],\"F\":\"P(S)\",\"S\":[97,98,99],\"x\":97}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0001","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={1, 2, 3}，F=P(S)，E={2}。E 的基數是多少？","answer":{"kind":"numeric","value":1,"explanation_zh":"E 有 1 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261219,"parameters":{"S":[1,2,3],"E":[2],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[2],\"F\":\"P(S)\",\"S\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0002","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={5, 6, 7}，F=P(S)，E={5, 7}。E 的基數是多少？","answer":{"kind":"numeric","value":2,"explanation_zh":"E 有 2 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261220,"parameters":{"S":[5,6,7],"E":[5,7],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[5,7],\"F\":\"P(S)\",\"S\":[5,6,7]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0003","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={9, 10, 11}，F=P(S)，E={10}。E 的基數是多少？","answer":{"kind":"numeric","value":1,"explanation_zh":"E 有 1 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261221,"parameters":{"S":[9,10,11],"E":[10],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[10],\"F\":\"P(S)\",\"S\":[9,10,11]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0004","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={13, 14, 15}，F=P(S)，E={13, 15}。E 的基數是多少？","answer":{"kind":"numeric","value":2,"explanation_zh":"E 有 2 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261222,"parameters":{"S":[13,14,15],"E":[13,15],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[13,15],\"F\":\"P(S)\",\"S\":[13,14,15]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0005","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={17, 18, 19}，F=P(S)，E={18}。E 的基數是多少？","answer":{"kind":"numeric","value":1,"explanation_zh":"E 有 1 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261223,"parameters":{"S":[17,18,19],"E":[18],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[18],\"F\":\"P(S)\",\"S\":[17,18,19]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0006","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={21, 22, 23}，F=P(S)，E={21, 23}。E 的基數是多少？","answer":{"kind":"numeric","value":2,"explanation_zh":"E 有 2 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261224,"parameters":{"S":[21,22,23],"E":[21,23],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[21,23],\"F\":\"P(S)\",\"S\":[21,22,23]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0007","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={25, 26, 27}，F=P(S)，E={26}。E 的基數是多少？","answer":{"kind":"numeric","value":1,"explanation_zh":"E 有 1 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261225,"parameters":{"S":[25,26,27],"E":[26],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[26],\"F\":\"P(S)\",\"S\":[25,26,27]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0008","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={29, 30, 31}，F=P(S)，E={29, 31}。E 的基數是多少？","answer":{"kind":"numeric","value":2,"explanation_zh":"E 有 2 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261226,"parameters":{"S":[29,30,31],"E":[29,31],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[29,31],\"F\":\"P(S)\",\"S\":[29,30,31]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0009","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={33, 34, 35}，F=P(S)，E={34}。E 的基數是多少？","answer":{"kind":"numeric","value":1,"explanation_zh":"E 有 1 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261227,"parameters":{"S":[33,34,35],"E":[34],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[34],\"F\":\"P(S)\",\"S\":[33,34,35]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0010","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={37, 38, 39}，F=P(S)，E={37, 39}。E 的基數是多少？","answer":{"kind":"numeric","value":2,"explanation_zh":"E 有 2 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261228,"parameters":{"S":[37,38,39],"E":[37,39],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[37,39],\"F\":\"P(S)\",\"S\":[37,38,39]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0011","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={41, 42, 43}，F=P(S)，E={42}。E 的基數是多少？","answer":{"kind":"numeric","value":1,"explanation_zh":"E 有 1 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261229,"parameters":{"S":[41,42,43],"E":[42],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[42],\"F\":\"P(S)\",\"S\":[41,42,43]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0012","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={45, 46, 47}，F=P(S)，E={45, 47}。E 的基數是多少？","answer":{"kind":"numeric","value":2,"explanation_zh":"E 有 2 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261230,"parameters":{"S":[45,46,47],"E":[45,47],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[45,47],\"F\":\"P(S)\",\"S\":[45,46,47]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0013","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={49, 50, 51}，F=P(S)，E={50}。E 的基數是多少？","answer":{"kind":"numeric","value":1,"explanation_zh":"E 有 1 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261231,"parameters":{"S":[49,50,51],"E":[50],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[50],\"F\":\"P(S)\",\"S\":[49,50,51]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0014","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={53, 54, 55}，F=P(S)，E={53, 55}。E 的基數是多少？","answer":{"kind":"numeric","value":2,"explanation_zh":"E 有 2 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261232,"parameters":{"S":[53,54,55],"E":[53,55],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[53,55],\"F\":\"P(S)\",\"S\":[53,54,55]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260918-finite-event-cardinality-0015","batch_id":"batch-20260918-finite-events","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"qf-finite-event-cardinality","stem_zh":"S={57, 58, 59}，F=P(S)，E={58}。E 的基數是多少？","answer":{"kind":"numeric","value":1,"explanation_zh":"E 有 1 個不同結果；這不是機率。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件基數"]},"variant":{"family_id":"qf-finite-event-cardinality","seed":20261233,"parameters":{"S":[57,58,59],"E":[58],"F":"P(S)","semantic_template":"qf-finite-event-cardinality/{\"E\":[58],\"F\":\"P(S)\",\"S\":[57,58,59]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-18","contract_version":"ocme-question-factory-v0.1"}}
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