{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0001","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=1；F=P(S)；E=[]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([], [0], 1)","explanation_zh":"事件與補事件分割=([], [0], 1)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136001,"parameters":{"n":1,"E":[],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[1,[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0002","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=1；F=P(S)；E=[0]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0], [], 1)","explanation_zh":"事件與補事件分割=([0], [], 1)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136002,"parameters":{"n":1,"E":[0],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[1,[0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0003","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0], [1, 2, 3, 4], 5)","explanation_zh":"事件與補事件分割=([0], [1, 2, 3, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136003,"parameters":{"n":5,"E":[0],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0004","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[1]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([1], [0, 2, 3, 4], 5)","explanation_zh":"事件與補事件分割=([1], [0, 2, 3, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136004,"parameters":{"n":5,"E":[1],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0005","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 1]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 1], [2, 3, 4], 5)","explanation_zh":"事件與補事件分割=([0, 1], [2, 3, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136005,"parameters":{"n":5,"E":[0,1],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0006","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[2]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([2], [0, 1, 3, 4], 5)","explanation_zh":"事件與補事件分割=([2], [0, 1, 3, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136006,"parameters":{"n":5,"E":[2],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0007","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 2]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 2], [1, 3, 4], 5)","explanation_zh":"事件與補事件分割=([0, 2], [1, 3, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136007,"parameters":{"n":5,"E":[0,2],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0008","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[1, 2]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([1, 2], [0, 3, 4], 5)","explanation_zh":"事件與補事件分割=([1, 2], [0, 3, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136008,"parameters":{"n":5,"E":[1,2],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[1,2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0009","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 1, 2]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 1, 2], [3, 4], 5)","explanation_zh":"事件與補事件分割=([0, 1, 2], [3, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136009,"parameters":{"n":5,"E":[0,1,2],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,1,2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0010","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[3]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([3], [0, 1, 2, 4], 5)","explanation_zh":"事件與補事件分割=([3], [0, 1, 2, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136010,"parameters":{"n":5,"E":[3],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0011","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 3]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 3], [1, 2, 4], 5)","explanation_zh":"事件與補事件分割=([0, 3], [1, 2, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136011,"parameters":{"n":5,"E":[0,3],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0012","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[1, 3]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([1, 3], [0, 2, 4], 5)","explanation_zh":"事件與補事件分割=([1, 3], [0, 2, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136012,"parameters":{"n":5,"E":[1,3],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0013","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 1, 3]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 1, 3], [2, 4], 5)","explanation_zh":"事件與補事件分割=([0, 1, 3], [2, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136013,"parameters":{"n":5,"E":[0,1,3],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0014","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[2, 3]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([2, 3], [0, 1, 4], 5)","explanation_zh":"事件與補事件分割=([2, 3], [0, 1, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136014,"parameters":{"n":5,"E":[2,3],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[2,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0015","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 2, 3]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 2, 3], [1, 4], 5)","explanation_zh":"事件與補事件分割=([0, 2, 3], [1, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136015,"parameters":{"n":5,"E":[0,2,3],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,2,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0016","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[1, 2, 3]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([1, 2, 3], [0, 4], 5)","explanation_zh":"事件與補事件分割=([1, 2, 3], [0, 4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136016,"parameters":{"n":5,"E":[1,2,3],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[1,2,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0017","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 1, 2, 3]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 1, 2, 3], [4], 5)","explanation_zh":"事件與補事件分割=([0, 1, 2, 3], [4], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136017,"parameters":{"n":5,"E":[0,1,2,3],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,1,2,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0018","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[4]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([4], [0, 1, 2, 3], 5)","explanation_zh":"事件與補事件分割=([4], [0, 1, 2, 3], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136018,"parameters":{"n":5,"E":[4],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0019","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 4]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 4], [1, 2, 3], 5)","explanation_zh":"事件與補事件分割=([0, 4], [1, 2, 3], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136019,"parameters":{"n":5,"E":[0,4],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0020","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[1, 4]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([1, 4], [0, 2, 3], 5)","explanation_zh":"事件與補事件分割=([1, 4], [0, 2, 3], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136020,"parameters":{"n":5,"E":[1,4],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[1,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0021","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 1, 4]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 1, 4], [2, 3], 5)","explanation_zh":"事件與補事件分割=([0, 1, 4], [2, 3], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136021,"parameters":{"n":5,"E":[0,1,4],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,1,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0022","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[2, 4]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([2, 4], [0, 1, 3], 5)","explanation_zh":"事件與補事件分割=([2, 4], [0, 1, 3], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136022,"parameters":{"n":5,"E":[2,4],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[2,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0023","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 2, 4]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 2, 4], [1, 3], 5)","explanation_zh":"事件與補事件分割=([0, 2, 4], [1, 3], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136023,"parameters":{"n":5,"E":[0,2,4],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,2,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0024","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[1, 2, 4]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([1, 2, 4], [0, 3], 5)","explanation_zh":"事件與補事件分割=([1, 2, 4], [0, 3], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136024,"parameters":{"n":5,"E":[1,2,4],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[1,2,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0025","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"事件與補事件的完整分割","stem_zh":"S=Fin(n)，n=5；F=P(S)；E=[0, 1, 2, 4]⊆S。依序列 (遞增E, 遞增S\\E, n)。","answer":{"kind":"expression","value":"([0, 1, 2, 4], [3], 5)","explanation_zh":"事件與補事件分割=([0, 1, 2, 4], [3], 5)。依聲明的完整事件族在S內取補；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["事件與補事件的完整分割"]},"variant":{"family_id":"qf-density13-event-complement-partition","seed":202610136025,"parameters":{"n":5,"E":[0,1,2,4],"event_model":"full_powerset","operation":"density13_event_complement_partition","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-complement-partition/[5,[0,1,2,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0026","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=1；F=P(S)；A=[]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([], [], [0])","explanation_zh":"聯交與外補事件=([], [], [0])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136026,"parameters":{"n":1,"A":[],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[1,[],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0027","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=1；F=P(S)；A=[0]、B=[0]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0], [0], [])","explanation_zh":"聯交與外補事件=([0], [0], [])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136027,"parameters":{"n":1,"A":[0],"B":[0],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[1,[0],[0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0028","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0], [], [1, 2, 3, 4])","explanation_zh":"聯交與外補事件=([0], [], [1, 2, 3, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136028,"parameters":{"n":5,"A":[0],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0029","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[1]、B=[1]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([1], [1], [0, 2, 3, 4])","explanation_zh":"聯交與外補事件=([1], [1], [0, 2, 3, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136029,"parameters":{"n":5,"A":[1],"B":[1],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[1],[1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0030","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 1]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 1], [], [2, 3, 4])","explanation_zh":"聯交與外補事件=([0, 1], [], [2, 3, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136030,"parameters":{"n":5,"A":[0,1],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,1],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0031","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[2]、B=[2]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([2], [2], [0, 1, 3, 4])","explanation_zh":"聯交與外補事件=([2], [2], [0, 1, 3, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136031,"parameters":{"n":5,"A":[2],"B":[2],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[2],[2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0032","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 2]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 2], [], [1, 3, 4])","explanation_zh":"聯交與外補事件=([0, 2], [], [1, 3, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136032,"parameters":{"n":5,"A":[0,2],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,2],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0033","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[1, 2]、B=[1]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([1, 2], [1], [0, 3, 4])","explanation_zh":"聯交與外補事件=([1, 2], [1], [0, 3, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136033,"parameters":{"n":5,"A":[1,2],"B":[1],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[1,2],[1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0034","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 1, 2]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 1, 2], [], [3, 4])","explanation_zh":"聯交與外補事件=([0, 1, 2], [], [3, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136034,"parameters":{"n":5,"A":[0,1,2],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,1,2],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0035","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[3]、B=[3]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([3], [3], [0, 1, 2, 4])","explanation_zh":"聯交與外補事件=([3], [3], [0, 1, 2, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136035,"parameters":{"n":5,"A":[3],"B":[3],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[3],[3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0036","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 3]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 3], [], [1, 2, 4])","explanation_zh":"聯交與外補事件=([0, 3], [], [1, 2, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136036,"parameters":{"n":5,"A":[0,3],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,3],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0037","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[1, 3]、B=[1]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([1, 3], [1], [0, 2, 4])","explanation_zh":"聯交與外補事件=([1, 3], [1], [0, 2, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136037,"parameters":{"n":5,"A":[1,3],"B":[1],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[1,3],[1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0038","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 1, 3]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 1, 3], [], [2, 4])","explanation_zh":"聯交與外補事件=([0, 1, 3], [], [2, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136038,"parameters":{"n":5,"A":[0,1,3],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,1,3],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0039","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[2, 3]、B=[2]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([2, 3], [2], [0, 1, 4])","explanation_zh":"聯交與外補事件=([2, 3], [2], [0, 1, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136039,"parameters":{"n":5,"A":[2,3],"B":[2],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[2,3],[2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0040","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 2, 3]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 2, 3], [], [1, 4])","explanation_zh":"聯交與外補事件=([0, 2, 3], [], [1, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136040,"parameters":{"n":5,"A":[0,2,3],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,2,3],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0041","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[1, 2, 3]、B=[1]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([1, 2, 3], [1], [0, 4])","explanation_zh":"聯交與外補事件=([1, 2, 3], [1], [0, 4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136041,"parameters":{"n":5,"A":[1,2,3],"B":[1],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[1,2,3],[1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0042","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 1, 2, 3]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 1, 2, 3], [], [4])","explanation_zh":"聯交與外補事件=([0, 1, 2, 3], [], [4])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136042,"parameters":{"n":5,"A":[0,1,2,3],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,1,2,3],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0043","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[4]、B=[4]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([4], [4], [0, 1, 2, 3])","explanation_zh":"聯交與外補事件=([4], [4], [0, 1, 2, 3])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136043,"parameters":{"n":5,"A":[4],"B":[4],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[4],[4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0044","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 4]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 4], [], [1, 2, 3])","explanation_zh":"聯交與外補事件=([0, 4], [], [1, 2, 3])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136044,"parameters":{"n":5,"A":[0,4],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,4],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0045","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[1, 4]、B=[1]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([1, 4], [1], [0, 2, 3])","explanation_zh":"聯交與外補事件=([1, 4], [1], [0, 2, 3])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136045,"parameters":{"n":5,"A":[1,4],"B":[1],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[1,4],[1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0046","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 1, 4]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 1, 4], [], [2, 3])","explanation_zh":"聯交與外補事件=([0, 1, 4], [], [2, 3])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136046,"parameters":{"n":5,"A":[0,1,4],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,1,4],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0047","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[2, 4]、B=[2]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([2, 4], [2], [0, 1, 3])","explanation_zh":"聯交與外補事件=([2, 4], [2], [0, 1, 3])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136047,"parameters":{"n":5,"A":[2,4],"B":[2],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[2,4],[2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0048","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 2, 4]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 2, 4], [], [1, 3])","explanation_zh":"聯交與外補事件=([0, 2, 4], [], [1, 3])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136048,"parameters":{"n":5,"A":[0,2,4],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,2,4],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0049","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[1, 2, 4]、B=[1]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([1, 2, 4], [1], [0, 3])","explanation_zh":"聯交與外補事件=([1, 2, 4], [1], [0, 3])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136049,"parameters":{"n":5,"A":[1,2,4],"B":[1],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[1,2,4],[1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0050","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"聯交事件與聯集外補","stem_zh":"S=Fin(n)，n=5；F=P(S)；A=[0, 1, 2, 4]、B=[]均在S內。依序列 (A∪B, A∩B, S\\(A∪B))，各去重遞增。","answer":{"kind":"expression","value":"([0, 1, 2, 4], [], [3])","explanation_zh":"聯交與外補事件=([0, 1, 2, 4], [], [3])。枚舉同一S的聯交與外補，不混同裸結果與事件；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["聯交事件與聯集外補"]},"variant":{"family_id":"qf-density13-event-boolean-algebra-pair","seed":202610136050,"parameters":{"n":5,"A":[0,1,2,4],"B":[],"event_model":"full_powerset","operation":"density13_event_boolean_algebra_pair","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-boolean-algebra-pair/[5,[0,1,2,4],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0051","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=1；F為完整分塊的聯集族；完整互斥非空blocks=[[0]]，候選E=[]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(是, [], [])","explanation_zh":"分塊事件資格與閉包=(是, [], [])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136051,"parameters":{"n":1,"blocks":[[0]],"E":[],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[true,[],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0052","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=3；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 1], [2]]，候選E=[0, 1]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(是, [], [0, 1])","explanation_zh":"分塊事件資格與閉包=(是, [], [0, 1])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136052,"parameters":{"n":3,"blocks":[[0,1],[2]],"E":[0,1],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[true,[],[0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0053","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=3；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 1], [2]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 1]], [0, 1])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 1]], [0, 1])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136053,"parameters":{"n":3,"blocks":[[0,1],[2]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,1]],[0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0054","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 2], [1], [3], [4], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 2]], [0, 2])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 2]], [0, 2])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136054,"parameters":{"n":8,"blocks":[[0,2],[1],[3],[4],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,2]],[0,2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0055","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[1, 2], [0], [3], [4], [5], [6], [7]]，候選E=[1]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[1, 2]], [1, 2])","explanation_zh":"分塊事件資格與閉包=(否, [[1, 2]], [1, 2])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136055,"parameters":{"n":8,"blocks":[[1,2],[0],[3],[4],[5],[6],[7]],"E":[1],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[1,2]],[1,2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0056","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 1, 2], [3], [4], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 1, 2]], [0, 1, 2])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 1, 2]], [0, 1, 2])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136056,"parameters":{"n":8,"blocks":[[0,1,2],[3],[4],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,1,2]],[0,1,2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0057","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 3], [1], [2], [4], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 3]], [0, 3])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 3]], [0, 3])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136057,"parameters":{"n":8,"blocks":[[0,3],[1],[2],[4],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,3]],[0,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0058","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[1, 3], [0], [2], [4], [5], [6], [7]]，候選E=[1]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[1, 3]], [1, 3])","explanation_zh":"分塊事件資格與閉包=(否, [[1, 3]], [1, 3])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136058,"parameters":{"n":8,"blocks":[[1,3],[0],[2],[4],[5],[6],[7]],"E":[1],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[1,3]],[1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0059","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 1, 3], [2], [4], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 1, 3]], [0, 1, 3])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 1, 3]], [0, 1, 3])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136059,"parameters":{"n":8,"blocks":[[0,1,3],[2],[4],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,1,3]],[0,1,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0060","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[2, 3], [0], [1], [4], [5], [6], [7]]，候選E=[2]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[2, 3]], [2, 3])","explanation_zh":"分塊事件資格與閉包=(否, [[2, 3]], [2, 3])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136060,"parameters":{"n":8,"blocks":[[2,3],[0],[1],[4],[5],[6],[7]],"E":[2],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[2,3]],[2,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0061","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 2, 3], [1], [4], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 2, 3]], [0, 2, 3])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 2, 3]], [0, 2, 3])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136061,"parameters":{"n":8,"blocks":[[0,2,3],[1],[4],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,2,3]],[0,2,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0062","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[1, 2, 3], [0], [4], [5], [6], [7]]，候選E=[1]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[1, 2, 3]], [1, 2, 3])","explanation_zh":"分塊事件資格與閉包=(否, [[1, 2, 3]], [1, 2, 3])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136062,"parameters":{"n":8,"blocks":[[1,2,3],[0],[4],[5],[6],[7]],"E":[1],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[1,2,3]],[1,2,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0063","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 1, 2, 3], [4], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 1, 2, 3]], [0, 1, 2, 3])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 1, 2, 3]], [0, 1, 2, 3])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136063,"parameters":{"n":8,"blocks":[[0,1,2,3],[4],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,1,2,3]],[0,1,2,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0064","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 4], [1], [2], [3], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 4]], [0, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 4]], [0, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136064,"parameters":{"n":8,"blocks":[[0,4],[1],[2],[3],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,4]],[0,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0065","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[1, 4], [0], [2], [3], [5], [6], [7]]，候選E=[1]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[1, 4]], [1, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[1, 4]], [1, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136065,"parameters":{"n":8,"blocks":[[1,4],[0],[2],[3],[5],[6],[7]],"E":[1],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[1,4]],[1,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0066","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 1, 4], [2], [3], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 1, 4]], [0, 1, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 1, 4]], [0, 1, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136066,"parameters":{"n":8,"blocks":[[0,1,4],[2],[3],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,1,4]],[0,1,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0067","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[2, 4], [0], [1], [3], [5], [6], [7]]，候選E=[2]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[2, 4]], [2, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[2, 4]], [2, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136067,"parameters":{"n":8,"blocks":[[2,4],[0],[1],[3],[5],[6],[7]],"E":[2],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[2,4]],[2,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0068","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 2, 4], [1], [3], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 2, 4]], [0, 2, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 2, 4]], [0, 2, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136068,"parameters":{"n":8,"blocks":[[0,2,4],[1],[3],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,2,4]],[0,2,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0069","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[1, 2, 4], [0], [3], [5], [6], [7]]，候選E=[1]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[1, 2, 4]], [1, 2, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[1, 2, 4]], [1, 2, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136069,"parameters":{"n":8,"blocks":[[1,2,4],[0],[3],[5],[6],[7]],"E":[1],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[1,2,4]],[1,2,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0070","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 1, 2, 4], [3], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 1, 2, 4]], [0, 1, 2, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 1, 2, 4]], [0, 1, 2, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136070,"parameters":{"n":8,"blocks":[[0,1,2,4],[3],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,1,2,4]],[0,1,2,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0071","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[3, 4], [0], [1], [2], [5], [6], [7]]，候選E=[3]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[3, 4]], [3, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[3, 4]], [3, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136071,"parameters":{"n":8,"blocks":[[3,4],[0],[1],[2],[5],[6],[7]],"E":[3],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[3,4]],[3,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0072","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 3, 4], [1], [2], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 3, 4]], [0, 3, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 3, 4]], [0, 3, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136072,"parameters":{"n":8,"blocks":[[0,3,4],[1],[2],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,3,4]],[0,3,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0073","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[1, 3, 4], [0], [2], [5], [6], [7]]，候選E=[1]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[1, 3, 4]], [1, 3, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[1, 3, 4]], [1, 3, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136073,"parameters":{"n":8,"blocks":[[1,3,4],[0],[2],[5],[6],[7]],"E":[1],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[1,3,4]],[1,3,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0074","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[0, 1, 3, 4], [2], [5], [6], [7]]，候選E=[0]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[0, 1, 3, 4]], [0, 1, 3, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[0, 1, 3, 4]], [0, 1, 3, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136074,"parameters":{"n":8,"blocks":[[0,1,3,4],[2],[5],[6],[7]],"E":[0],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[0,1,3,4]],[0,1,3,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0075","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"分塊聯集族的資格與最小閉包","stem_zh":"S=Fin(n)，n=8；F為完整分塊的聯集族；完整互斥非空blocks=[[2, 3, 4], [0], [1], [5], [6], [7]]，候選E=[2]⊆S。依序答 (E是否完整分塊聯集, 部分命中的分塊成員列表, 最小包含E的F集合)，塊內排序、塊外按數值字典序。","answer":{"kind":"expression","value":"(否, [[2, 3, 4]], [2, 3, 4])","explanation_zh":"分塊事件資格與閉包=(否, [[2, 3, 4]], [2, 3, 4])。每塊只准全取或全不取；閉包取所有有命中的整塊，整塊命中不列部分；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分塊聯集族的資格與最小閉包"]},"variant":{"family_id":"qf-density13-event-partition-family-qualification","seed":202610136075,"parameters":{"n":8,"blocks":[[2,3,4],[0],[1],[5],[6],[7]],"E":[2],"event_model":"partition_unions","operation":"density13_event_partition_family_qualification","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-partition-family-qualification/[false,[[2,3,4]],[2,3,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0076","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=1；F=P(S)；E=[]，有序outcomes=[]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([], [], 無)","explanation_zh":"觀測資格與首發生=([], [], 無)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136076,"parameters":{"n":1,"E":[],"outcomes":[],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0077","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 101, 102]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([否, 否, 否], [不合樣本, 不合樣本, 不合樣本], 無)","explanation_zh":"觀測資格與首發生=([否, 否, 否], [不合樣本, 不合樣本, 不合樣本], 無)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136077,"parameters":{"n":3,"E":[1],"outcomes":[100,101,102],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"outside\",\"outside\",\"outside\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0078","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[0, 2, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 是], [假, 假, 假], 無)","explanation_zh":"觀測資格與首發生=([是, 是, 是], [假, 假, 假], 無)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136078,"parameters":{"n":3,"E":[1],"outcomes":[0,2,0],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"nonmember\",\"nonmember\",\"nonmember\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0079","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[1, 1, 1]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 是], [真, 真, 真], 0)","explanation_zh":"觀測資格與首發生=([是, 是, 是], [真, 真, 真], 0)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136079,"parameters":{"n":3,"E":[1],"outcomes":[1,1,1],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"member\",\"member\",\"member\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0080","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[0, 101, 102]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 否, 否], [假, 不合樣本, 不合樣本], 無)","explanation_zh":"觀測資格與首發生=([是, 否, 否], [假, 不合樣本, 不合樣本], 無)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136080,"parameters":{"n":3,"E":[1],"outcomes":[0,101,102],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"nonmember\",\"outside\",\"outside\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0081","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[1, 101, 102]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 否, 否], [真, 不合樣本, 不合樣本], 0)","explanation_zh":"觀測資格與首發生=([是, 否, 否], [真, 不合樣本, 不合樣本], 0)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136081,"parameters":{"n":3,"E":[1],"outcomes":[1,101,102],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"member\",\"outside\",\"outside\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0082","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 2, 102]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([否, 是, 否], [不合樣本, 假, 不合樣本], 無)","explanation_zh":"觀測資格與首發生=([否, 是, 否], [不合樣本, 假, 不合樣本], 無)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136082,"parameters":{"n":3,"E":[1],"outcomes":[100,2,102],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"outside\",\"nonmember\",\"outside\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0083","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[0, 2, 102]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 否], [假, 假, 不合樣本], 無)","explanation_zh":"觀測資格與首發生=([是, 是, 否], [假, 假, 不合樣本], 無)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136083,"parameters":{"n":3,"E":[1],"outcomes":[0,2,102],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"nonmember\",\"nonmember\",\"outside\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0084","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[1, 2, 102]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 否], [真, 假, 不合樣本], 0)","explanation_zh":"觀測資格與首發生=([是, 是, 否], [真, 假, 不合樣本], 0)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136084,"parameters":{"n":3,"E":[1],"outcomes":[1,2,102],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"member\",\"nonmember\",\"outside\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0085","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 1, 102]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([否, 是, 否], [不合樣本, 真, 不合樣本], 1)","explanation_zh":"觀測資格與首發生=([否, 是, 否], [不合樣本, 真, 不合樣本], 1)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136085,"parameters":{"n":3,"E":[1],"outcomes":[100,1,102],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"outside\",\"member\",\"outside\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0086","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[0, 1, 102]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 否], [假, 真, 不合樣本], 1)","explanation_zh":"觀測資格與首發生=([是, 是, 否], [假, 真, 不合樣本], 1)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136086,"parameters":{"n":3,"E":[1],"outcomes":[0,1,102],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"nonmember\",\"member\",\"outside\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0087","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[1, 1, 102]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 否], [真, 真, 不合樣本], 0)","explanation_zh":"觀測資格與首發生=([是, 是, 否], [真, 真, 不合樣本], 0)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136087,"parameters":{"n":3,"E":[1],"outcomes":[1,1,102],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"member\",\"member\",\"outside\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0088","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 101, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([否, 否, 是], [不合樣本, 不合樣本, 假], 無)","explanation_zh":"觀測資格與首發生=([否, 否, 是], [不合樣本, 不合樣本, 假], 無)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136088,"parameters":{"n":3,"E":[1],"outcomes":[100,101,0],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"outside\",\"outside\",\"nonmember\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0089","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[0, 101, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 否, 是], [假, 不合樣本, 假], 無)","explanation_zh":"觀測資格與首發生=([是, 否, 是], [假, 不合樣本, 假], 無)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136089,"parameters":{"n":3,"E":[1],"outcomes":[0,101,0],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"nonmember\",\"outside\",\"nonmember\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0090","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[1, 101, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 否, 是], [真, 不合樣本, 假], 0)","explanation_zh":"觀測資格與首發生=([是, 否, 是], [真, 不合樣本, 假], 0)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136090,"parameters":{"n":3,"E":[1],"outcomes":[1,101,0],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"member\",\"outside\",\"nonmember\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0091","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 2, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([否, 是, 是], [不合樣本, 假, 假], 無)","explanation_zh":"觀測資格與首發生=([否, 是, 是], [不合樣本, 假, 假], 無)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136091,"parameters":{"n":3,"E":[1],"outcomes":[100,2,0],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"outside\",\"nonmember\",\"nonmember\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0092","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[1, 2, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 是], [真, 假, 假], 0)","explanation_zh":"觀測資格與首發生=([是, 是, 是], [真, 假, 假], 0)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136092,"parameters":{"n":3,"E":[1],"outcomes":[1,2,0],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"member\",\"nonmember\",\"nonmember\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0093","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 1, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([否, 是, 是], [不合樣本, 真, 假], 1)","explanation_zh":"觀測資格與首發生=([否, 是, 是], [不合樣本, 真, 假], 1)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136093,"parameters":{"n":3,"E":[1],"outcomes":[100,1,0],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"outside\",\"member\",\"nonmember\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0094","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[0, 1, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 是], [假, 真, 假], 1)","explanation_zh":"觀測資格與首發生=([是, 是, 是], [假, 真, 假], 1)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136094,"parameters":{"n":3,"E":[1],"outcomes":[0,1,0],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"nonmember\",\"member\",\"nonmember\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0095","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[1, 1, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 是], [真, 真, 假], 0)","explanation_zh":"觀測資格與首發生=([是, 是, 是], [真, 真, 假], 0)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136095,"parameters":{"n":3,"E":[1],"outcomes":[1,1,0],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"member\",\"member\",\"nonmember\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0096","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 101, 1]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([否, 否, 是], [不合樣本, 不合樣本, 真], 2)","explanation_zh":"觀測資格與首發生=([否, 否, 是], [不合樣本, 不合樣本, 真], 2)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136096,"parameters":{"n":3,"E":[1],"outcomes":[100,101,1],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"outside\",\"outside\",\"member\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0097","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[0, 101, 1]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 否, 是], [假, 不合樣本, 真], 2)","explanation_zh":"觀測資格與首發生=([是, 否, 是], [假, 不合樣本, 真], 2)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136097,"parameters":{"n":3,"E":[1],"outcomes":[0,101,1],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"nonmember\",\"outside\",\"member\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0098","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[1, 101, 1]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 否, 是], [真, 不合樣本, 真], 0)","explanation_zh":"觀測資格與首發生=([是, 否, 是], [真, 不合樣本, 真], 0)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136098,"parameters":{"n":3,"E":[1],"outcomes":[1,101,1],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"member\",\"outside\",\"member\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0099","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 2, 1]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([否, 是, 是], [不合樣本, 假, 真], 2)","explanation_zh":"觀測資格與首發生=([否, 是, 是], [不合樣本, 假, 真], 2)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136099,"parameters":{"n":3,"E":[1],"outcomes":[100,2,1],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"outside\",\"nonmember\",\"member\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r06-event-0100","batch_id":"batch-20261009-advance-20261013-r06-event-foundations","language":"zh-Hant","source_mko_ids":["mko-event"],"title_zh":"觀測候選資格與第一個合法發生","stem_zh":"S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[0, 2, 1]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。","answer":{"kind":"expression","value":"([是, 是, 是], [假, 假, 真], 2)","explanation_zh":"觀測資格與首發生=([是, 是, 是], [假, 假, 真], 2)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測候選資格與第一個合法發生"]},"variant":{"family_id":"qf-density13-event-occurrence-first-hit","seed":202610136100,"parameters":{"n":3,"E":[1],"outcomes":[0,2,1],"event_model":"full_powerset","operation":"density13_event_occurrence_first_hit","domain":"finite_declared_event_family","semantic_template":"qf-density13-event-occurrence-first-hit/[\"nonmember\",\"nonmember\",\"member\"]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}