{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0001","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={1, 3, 5}，B={3, 4, 6}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1, 3, 4, 5, 6}","explanation_zh":"元素 3 同時在 A 與 B 中，但聯集只保留一次；結果為 {1, 3, 4, 5, 6}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260915,"parameters":{"A":[1,3,5],"B":[3,4,6],"semantic_template":"qf-finite-set-union/{\"A\":[1,3,5],\"B\":[3,4,6]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0002","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={11, 13, 15}，B={13, 14, 16}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{11, 13, 14, 15, 16}","explanation_zh":"元素 13 同時在 A 與 B 中，但聯集只保留一次；結果為 {11, 13, 14, 15, 16}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260916,"parameters":{"A":[11,13,15],"B":[13,14,16],"semantic_template":"qf-finite-set-union/{\"A\":[11,13,15],\"B\":[13,14,16]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0003","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={21, 23, 25}，B={23, 24, 26}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{21, 23, 24, 25, 26}","explanation_zh":"元素 23 同時在 A 與 B 中，但聯集只保留一次；結果為 {21, 23, 24, 25, 26}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260917,"parameters":{"A":[21,23,25],"B":[23,24,26],"semantic_template":"qf-finite-set-union/{\"A\":[21,23,25],\"B\":[23,24,26]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0004","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={31, 33, 35}，B={33, 34, 36}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{31, 33, 34, 35, 36}","explanation_zh":"元素 33 同時在 A 與 B 中，但聯集只保留一次；結果為 {31, 33, 34, 35, 36}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260918,"parameters":{"A":[31,33,35],"B":[33,34,36],"semantic_template":"qf-finite-set-union/{\"A\":[31,33,35],\"B\":[33,34,36]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0005","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={41, 43, 45}，B={43, 44, 46}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{41, 43, 44, 45, 46}","explanation_zh":"元素 43 同時在 A 與 B 中，但聯集只保留一次；結果為 {41, 43, 44, 45, 46}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260919,"parameters":{"A":[41,43,45],"B":[43,44,46],"semantic_template":"qf-finite-set-union/{\"A\":[41,43,45],\"B\":[43,44,46]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0006","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={51, 53, 55}，B={53, 54, 56}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{51, 53, 54, 55, 56}","explanation_zh":"元素 53 同時在 A 與 B 中，但聯集只保留一次；結果為 {51, 53, 54, 55, 56}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260920,"parameters":{"A":[51,53,55],"B":[53,54,56],"semantic_template":"qf-finite-set-union/{\"A\":[51,53,55],\"B\":[53,54,56]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0007","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={61, 63, 65}，B={63, 64, 66}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{61, 63, 64, 65, 66}","explanation_zh":"元素 63 同時在 A 與 B 中，但聯集只保留一次；結果為 {61, 63, 64, 65, 66}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260921,"parameters":{"A":[61,63,65],"B":[63,64,66],"semantic_template":"qf-finite-set-union/{\"A\":[61,63,65],\"B\":[63,64,66]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0008","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={71, 73, 75}，B={73, 74, 76}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{71, 73, 74, 75, 76}","explanation_zh":"元素 73 同時在 A 與 B 中，但聯集只保留一次；結果為 {71, 73, 74, 75, 76}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260922,"parameters":{"A":[71,73,75],"B":[73,74,76],"semantic_template":"qf-finite-set-union/{\"A\":[71,73,75],\"B\":[73,74,76]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0009","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={81, 83, 85}，B={83, 84, 86}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{81, 83, 84, 85, 86}","explanation_zh":"元素 83 同時在 A 與 B 中，但聯集只保留一次；結果為 {81, 83, 84, 85, 86}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260923,"parameters":{"A":[81,83,85],"B":[83,84,86],"semantic_template":"qf-finite-set-union/{\"A\":[81,83,85],\"B\":[83,84,86]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0010","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={91, 93, 95}，B={93, 94, 96}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{91, 93, 94, 95, 96}","explanation_zh":"元素 93 同時在 A 與 B 中，但聯集只保留一次；結果為 {91, 93, 94, 95, 96}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260924,"parameters":{"A":[91,93,95],"B":[93,94,96],"semantic_template":"qf-finite-set-union/{\"A\":[91,93,95],\"B\":[93,94,96]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0011","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={101, 103, 105}，B={103, 104, 106}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{101, 103, 104, 105, 106}","explanation_zh":"元素 103 同時在 A 與 B 中，但聯集只保留一次；結果為 {101, 103, 104, 105, 106}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260925,"parameters":{"A":[101,103,105],"B":[103,104,106],"semantic_template":"qf-finite-set-union/{\"A\":[101,103,105],\"B\":[103,104,106]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0012","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={111, 113, 115}，B={113, 114, 116}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{111, 113, 114, 115, 116}","explanation_zh":"元素 113 同時在 A 與 B 中，但聯集只保留一次；結果為 {111, 113, 114, 115, 116}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260926,"parameters":{"A":[111,113,115],"B":[113,114,116],"semantic_template":"qf-finite-set-union/{\"A\":[111,113,115],\"B\":[113,114,116]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0013","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={121, 123, 125}，B={123, 124, 126}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{121, 123, 124, 125, 126}","explanation_zh":"元素 123 同時在 A 與 B 中，但聯集只保留一次；結果為 {121, 123, 124, 125, 126}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260927,"parameters":{"A":[121,123,125],"B":[123,124,126],"semantic_template":"qf-finite-set-union/{\"A\":[121,123,125],\"B\":[123,124,126]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0014","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={131, 133, 135}，B={133, 134, 136}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{131, 133, 134, 135, 136}","explanation_zh":"元素 133 同時在 A 與 B 中，但聯集只保留一次；結果為 {131, 133, 134, 135, 136}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260928,"parameters":{"A":[131,133,135],"B":[133,134,136],"semantic_template":"qf-finite-set-union/{\"A\":[131,133,135],\"B\":[133,134,136]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0015","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={141, 143, 145}，B={143, 144, 146}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{141, 143, 144, 145, 146}","explanation_zh":"元素 143 同時在 A 與 B 中，但聯集只保留一次；結果為 {141, 143, 144, 145, 146}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260929,"parameters":{"A":[141,143,145],"B":[143,144,146],"semantic_template":"qf-finite-set-union/{\"A\":[141,143,145],\"B\":[143,144,146]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0016","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={151, 153, 155}，B={153, 154, 156}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{151, 153, 154, 155, 156}","explanation_zh":"元素 153 同時在 A 與 B 中，但聯集只保留一次；結果為 {151, 153, 154, 155, 156}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260930,"parameters":{"A":[151,153,155],"B":[153,154,156],"semantic_template":"qf-finite-set-union/{\"A\":[151,153,155],\"B\":[153,154,156]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0017","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={161, 163, 165}，B={163, 164, 166}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{161, 163, 164, 165, 166}","explanation_zh":"元素 163 同時在 A 與 B 中，但聯集只保留一次；結果為 {161, 163, 164, 165, 166}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260931,"parameters":{"A":[161,163,165],"B":[163,164,166],"semantic_template":"qf-finite-set-union/{\"A\":[161,163,165],\"B\":[163,164,166]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0018","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={171, 173, 175}，B={173, 174, 176}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{171, 173, 174, 175, 176}","explanation_zh":"元素 173 同時在 A 與 B 中，但聯集只保留一次；結果為 {171, 173, 174, 175, 176}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260932,"parameters":{"A":[171,173,175],"B":[173,174,176],"semantic_template":"qf-finite-set-union/{\"A\":[171,173,175],\"B\":[173,174,176]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0019","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={181, 183, 185}，B={183, 184, 186}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{181, 183, 184, 185, 186}","explanation_zh":"元素 183 同時在 A 與 B 中，但聯集只保留一次；結果為 {181, 183, 184, 185, 186}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260933,"parameters":{"A":[181,183,185],"B":[183,184,186],"semantic_template":"qf-finite-set-union/{\"A\":[181,183,185],\"B\":[183,184,186]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0020","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={191, 193, 195}，B={193, 194, 196}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{191, 193, 194, 195, 196}","explanation_zh":"元素 193 同時在 A 與 B 中，但聯集只保留一次；結果為 {191, 193, 194, 195, 196}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260934,"parameters":{"A":[191,193,195],"B":[193,194,196],"semantic_template":"qf-finite-set-union/{\"A\":[191,193,195],\"B\":[193,194,196]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0021","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={201, 203, 205}，B={203, 204, 206}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{201, 203, 204, 205, 206}","explanation_zh":"元素 203 同時在 A 與 B 中，但聯集只保留一次；結果為 {201, 203, 204, 205, 206}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260935,"parameters":{"A":[201,203,205],"B":[203,204,206],"semantic_template":"qf-finite-set-union/{\"A\":[201,203,205],\"B\":[203,204,206]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0022","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={211, 213, 215}，B={213, 214, 216}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{211, 213, 214, 215, 216}","explanation_zh":"元素 213 同時在 A 與 B 中，但聯集只保留一次；結果為 {211, 213, 214, 215, 216}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260936,"parameters":{"A":[211,213,215],"B":[213,214,216],"semantic_template":"qf-finite-set-union/{\"A\":[211,213,215],\"B\":[213,214,216]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0023","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={221, 223, 225}，B={223, 224, 226}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{221, 223, 224, 225, 226}","explanation_zh":"元素 223 同時在 A 與 B 中，但聯集只保留一次；結果為 {221, 223, 224, 225, 226}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260937,"parameters":{"A":[221,223,225],"B":[223,224,226],"semantic_template":"qf-finite-set-union/{\"A\":[221,223,225],\"B\":[223,224,226]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0024","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={231, 233, 235}，B={233, 234, 236}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{231, 233, 234, 235, 236}","explanation_zh":"元素 233 同時在 A 與 B 中，但聯集只保留一次；結果為 {231, 233, 234, 235, 236}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260938,"parameters":{"A":[231,233,235],"B":[233,234,236],"semantic_template":"qf-finite-set-union/{\"A\":[231,233,235],\"B\":[233,234,236]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-union-0025","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯集","stem_zh":"令 A={241, 243, 245}，B={243, 244, 246}。求 A∪B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{241, 243, 244, 245, 246}","explanation_zh":"元素 243 同時在 A 與 B 中，但聯集只保留一次；結果為 {241, 243, 244, 245, 246}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合聯集","外延相等"]},"variant":{"family_id":"qf-finite-set-union","seed":20260939,"parameters":{"A":[241,243,245],"B":[243,244,246],"semantic_template":"qf-finite-set-union/{\"A\":[241,243,245],\"B\":[243,244,246]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0001","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={301, 302, 304}，B={302, 304, 306}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{302, 304}","explanation_zh":"元素 302 同時屬於 A 與 B；交集為 {302, 304}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260940,"parameters":{"A":[301,302,304],"B":[302,304,306],"semantic_template":"qf-finite-set-intersection/{\"A\":[301,302,304],\"B\":[302,304,306]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0002","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={311, 312, 314}，B={313, 315, 316}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260941,"parameters":{"A":[311,312,314],"B":[313,315,316],"semantic_template":"qf-finite-set-intersection/{\"A\":[311,312,314],\"B\":[313,315,316]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0003","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={321, 322, 324}，B={322, 324, 326}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{322, 324}","explanation_zh":"元素 322 同時屬於 A 與 B；交集為 {322, 324}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260942,"parameters":{"A":[321,322,324],"B":[322,324,326],"semantic_template":"qf-finite-set-intersection/{\"A\":[321,322,324],\"B\":[322,324,326]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0004","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={331, 332, 334}，B={333, 335, 336}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260943,"parameters":{"A":[331,332,334],"B":[333,335,336],"semantic_template":"qf-finite-set-intersection/{\"A\":[331,332,334],\"B\":[333,335,336]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0005","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={341, 342, 344}，B={342, 344, 346}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{342, 344}","explanation_zh":"元素 342 同時屬於 A 與 B；交集為 {342, 344}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260944,"parameters":{"A":[341,342,344],"B":[342,344,346],"semantic_template":"qf-finite-set-intersection/{\"A\":[341,342,344],\"B\":[342,344,346]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0006","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={351, 352, 354}，B={353, 355, 356}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260945,"parameters":{"A":[351,352,354],"B":[353,355,356],"semantic_template":"qf-finite-set-intersection/{\"A\":[351,352,354],\"B\":[353,355,356]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0007","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={361, 362, 364}，B={362, 364, 366}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{362, 364}","explanation_zh":"元素 362 同時屬於 A 與 B；交集為 {362, 364}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260946,"parameters":{"A":[361,362,364],"B":[362,364,366],"semantic_template":"qf-finite-set-intersection/{\"A\":[361,362,364],\"B\":[362,364,366]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0008","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={371, 372, 374}，B={373, 375, 376}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260947,"parameters":{"A":[371,372,374],"B":[373,375,376],"semantic_template":"qf-finite-set-intersection/{\"A\":[371,372,374],\"B\":[373,375,376]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0009","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={381, 382, 384}，B={382, 384, 386}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{382, 384}","explanation_zh":"元素 382 同時屬於 A 與 B；交集為 {382, 384}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260948,"parameters":{"A":[381,382,384],"B":[382,384,386],"semantic_template":"qf-finite-set-intersection/{\"A\":[381,382,384],\"B\":[382,384,386]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0010","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={391, 392, 394}，B={393, 395, 396}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260949,"parameters":{"A":[391,392,394],"B":[393,395,396],"semantic_template":"qf-finite-set-intersection/{\"A\":[391,392,394],\"B\":[393,395,396]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0011","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={401, 402, 404}，B={402, 404, 406}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{402, 404}","explanation_zh":"元素 402 同時屬於 A 與 B；交集為 {402, 404}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260950,"parameters":{"A":[401,402,404],"B":[402,404,406],"semantic_template":"qf-finite-set-intersection/{\"A\":[401,402,404],\"B\":[402,404,406]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0012","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={411, 412, 414}，B={413, 415, 416}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260951,"parameters":{"A":[411,412,414],"B":[413,415,416],"semantic_template":"qf-finite-set-intersection/{\"A\":[411,412,414],\"B\":[413,415,416]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0013","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={421, 422, 424}，B={422, 424, 426}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{422, 424}","explanation_zh":"元素 422 同時屬於 A 與 B；交集為 {422, 424}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260952,"parameters":{"A":[421,422,424],"B":[422,424,426],"semantic_template":"qf-finite-set-intersection/{\"A\":[421,422,424],\"B\":[422,424,426]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0014","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={431, 432, 434}，B={433, 435, 436}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260953,"parameters":{"A":[431,432,434],"B":[433,435,436],"semantic_template":"qf-finite-set-intersection/{\"A\":[431,432,434],\"B\":[433,435,436]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0015","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={441, 442, 444}，B={442, 444, 446}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{442, 444}","explanation_zh":"元素 442 同時屬於 A 與 B；交集為 {442, 444}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260954,"parameters":{"A":[441,442,444],"B":[442,444,446],"semantic_template":"qf-finite-set-intersection/{\"A\":[441,442,444],\"B\":[442,444,446]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0016","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={451, 452, 454}，B={453, 455, 456}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260955,"parameters":{"A":[451,452,454],"B":[453,455,456],"semantic_template":"qf-finite-set-intersection/{\"A\":[451,452,454],\"B\":[453,455,456]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0017","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={461, 462, 464}，B={462, 464, 466}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{462, 464}","explanation_zh":"元素 462 同時屬於 A 與 B；交集為 {462, 464}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260956,"parameters":{"A":[461,462,464],"B":[462,464,466],"semantic_template":"qf-finite-set-intersection/{\"A\":[461,462,464],\"B\":[462,464,466]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0018","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={471, 472, 474}，B={473, 475, 476}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260957,"parameters":{"A":[471,472,474],"B":[473,475,476],"semantic_template":"qf-finite-set-intersection/{\"A\":[471,472,474],\"B\":[473,475,476]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0019","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={481, 482, 484}，B={482, 484, 486}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{482, 484}","explanation_zh":"元素 482 同時屬於 A 與 B；交集為 {482, 484}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260958,"parameters":{"A":[481,482,484],"B":[482,484,486],"semantic_template":"qf-finite-set-intersection/{\"A\":[481,482,484],\"B\":[482,484,486]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0020","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={491, 492, 494}，B={493, 495, 496}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260959,"parameters":{"A":[491,492,494],"B":[493,495,496],"semantic_template":"qf-finite-set-intersection/{\"A\":[491,492,494],\"B\":[493,495,496]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0021","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={501, 502, 504}，B={502, 504, 506}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{502, 504}","explanation_zh":"元素 502 同時屬於 A 與 B；交集為 {502, 504}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260960,"parameters":{"A":[501,502,504],"B":[502,504,506],"semantic_template":"qf-finite-set-intersection/{\"A\":[501,502,504],\"B\":[502,504,506]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0022","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={511, 512, 514}，B={513, 515, 516}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260961,"parameters":{"A":[511,512,514],"B":[513,515,516],"semantic_template":"qf-finite-set-intersection/{\"A\":[511,512,514],\"B\":[513,515,516]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0023","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={521, 522, 524}，B={522, 524, 526}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{522, 524}","explanation_zh":"元素 522 同時屬於 A 與 B；交集為 {522, 524}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260962,"parameters":{"A":[521,522,524],"B":[522,524,526],"semantic_template":"qf-finite-set-intersection/{\"A\":[521,522,524],\"B\":[522,524,526]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0024","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={531, 532, 534}，B={533, 535, 536}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"∅","explanation_zh":"沒有元素同時屬於 A 與 B，因此交集明確為 ∅。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260963,"parameters":{"A":[531,532,534],"B":[533,535,536],"semantic_template":"qf-finite-set-intersection/{\"A\":[531,532,534],\"B\":[533,535,536]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-intersection-0025","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合交集","stem_zh":"令 A={541, 542, 544}，B={542, 544, 546}。求 A∩B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{542, 544}","explanation_zh":"元素 542 同時屬於 A 與 B；交集為 {542, 544}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合交集","外延相等"]},"variant":{"family_id":"qf-finite-set-intersection","seed":20260964,"parameters":{"A":[541,542,544],"B":[542,544,546],"semantic_template":"qf-finite-set-intersection/{\"A\":[541,542,544],\"B\":[542,544,546]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0001","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={601, 602, 604, 606}，B={602, 605, 606}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{601, 604}","explanation_zh":"601 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {605}，不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260965,"parameters":{"A":[601,602,604,606],"B":[602,605,606],"semantic_template":"qf-finite-set-difference/{\"A\":[601,602,604,606],\"B\":[602,605,606]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0002","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={611, 612, 614, 616}，B={612, 615, 616}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{611, 614}","explanation_zh":"611 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {615}，不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260966,"parameters":{"A":[611,612,614,616],"B":[612,615,616],"semantic_template":"qf-finite-set-difference/{\"A\":[611,612,614,616],\"B\":[612,615,616]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0003","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={621, 622, 624, 626}，B={622, 625, 626}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{621, 624}","explanation_zh":"621 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {625}，不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260967,"parameters":{"A":[621,622,624,626],"B":[622,625,626],"semantic_template":"qf-finite-set-difference/{\"A\":[621,622,624,626],\"B\":[622,625,626]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0004","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={631, 632, 634, 636}，B={632, 635, 636}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{631, 634}","explanation_zh":"631 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {635}，不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260968,"parameters":{"A":[631,632,634,636],"B":[632,635,636],"semantic_template":"qf-finite-set-difference/{\"A\":[631,632,634,636],\"B\":[632,635,636]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0005","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={641, 642, 644, 646}，B={642, 645, 646}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{641, 644}","explanation_zh":"641 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {645}，不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260969,"parameters":{"A":[641,642,644,646],"B":[642,645,646],"semantic_template":"qf-finite-set-difference/{\"A\":[641,642,644,646],\"B\":[642,645,646]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0006","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={651, 652, 654, 656}，B={652, 655, 656}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{651, 654}","explanation_zh":"651 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {655}，不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260970,"parameters":{"A":[651,652,654,656],"B":[652,655,656],"semantic_template":"qf-finite-set-difference/{\"A\":[651,652,654,656],\"B\":[652,655,656]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0007","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={661, 662, 664, 666}，B={662, 665, 666}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{661, 664}","explanation_zh":"661 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {665}，不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260971,"parameters":{"A":[661,662,664,666],"B":[662,665,666],"semantic_template":"qf-finite-set-difference/{\"A\":[661,662,664,666],\"B\":[662,665,666]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0008","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={671, 672, 674, 676}，B={672, 675, 676}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{671, 674}","explanation_zh":"671 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {675}，不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260972,"parameters":{"A":[671,672,674,676],"B":[672,675,676],"semantic_template":"qf-finite-set-difference/{\"A\":[671,672,674,676],\"B\":[672,675,676]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0009","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={681, 682, 684, 686}，B={682, 685, 686}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{681, 684}","explanation_zh":"681 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {685}，不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260973,"parameters":{"A":[681,682,684,686],"B":[682,685,686],"semantic_template":"qf-finite-set-difference/{\"A\":[681,682,684,686],\"B\":[682,685,686]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0010","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={691, 692, 694, 696}，B={692, 695, 696}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{691, 694}","explanation_zh":"691 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {695}，不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260974,"parameters":{"A":[691,692,694,696],"B":[692,695,696],"semantic_template":"qf-finite-set-difference/{\"A\":[691,692,694,696],\"B\":[692,695,696]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0011","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={701, 702, 704, 706}，B={702, 705, 706}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{701, 704}","explanation_zh":"701 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {705}，不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260975,"parameters":{"A":[701,702,704,706],"B":[702,705,706],"semantic_template":"qf-finite-set-difference/{\"A\":[701,702,704,706],\"B\":[702,705,706]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0012","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={711, 712, 714, 716}，B={712, 715, 716}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{711, 714}","explanation_zh":"711 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {715}，不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260976,"parameters":{"A":[711,712,714,716],"B":[712,715,716],"semantic_template":"qf-finite-set-difference/{\"A\":[711,712,714,716],\"B\":[712,715,716]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0013","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={721, 722, 724, 726}，B={722, 725, 726}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{721, 724}","explanation_zh":"721 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {725}，不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260977,"parameters":{"A":[721,722,724,726],"B":[722,725,726],"semantic_template":"qf-finite-set-difference/{\"A\":[721,722,724,726],\"B\":[722,725,726]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0014","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={731, 732, 734, 736}，B={732, 735, 736}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{731, 734}","explanation_zh":"731 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {735}，不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260978,"parameters":{"A":[731,732,734,736],"B":[732,735,736],"semantic_template":"qf-finite-set-difference/{\"A\":[731,732,734,736],\"B\":[732,735,736]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0015","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={741, 742, 744, 746}，B={742, 745, 746}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{741, 744}","explanation_zh":"741 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {745}，不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260979,"parameters":{"A":[741,742,744,746],"B":[742,745,746],"semantic_template":"qf-finite-set-difference/{\"A\":[741,742,744,746],\"B\":[742,745,746]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0016","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={751, 752, 754, 756}，B={752, 755, 756}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{751, 754}","explanation_zh":"751 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {755}，不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260980,"parameters":{"A":[751,752,754,756],"B":[752,755,756],"semantic_template":"qf-finite-set-difference/{\"A\":[751,752,754,756],\"B\":[752,755,756]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0017","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={761, 762, 764, 766}，B={762, 765, 766}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{761, 764}","explanation_zh":"761 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {765}，不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260981,"parameters":{"A":[761,762,764,766],"B":[762,765,766],"semantic_template":"qf-finite-set-difference/{\"A\":[761,762,764,766],\"B\":[762,765,766]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0018","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={771, 772, 774, 776}，B={772, 775, 776}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{771, 774}","explanation_zh":"771 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {775}，不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260982,"parameters":{"A":[771,772,774,776],"B":[772,775,776],"semantic_template":"qf-finite-set-difference/{\"A\":[771,772,774,776],\"B\":[772,775,776]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0019","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={781, 782, 784, 786}，B={782, 785, 786}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{781, 784}","explanation_zh":"781 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {785}，不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260983,"parameters":{"A":[781,782,784,786],"B":[782,785,786],"semantic_template":"qf-finite-set-difference/{\"A\":[781,782,784,786],\"B\":[782,785,786]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0020","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={791, 792, 794, 796}，B={792, 795, 796}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{791, 794}","explanation_zh":"791 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {795}，不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260984,"parameters":{"A":[791,792,794,796],"B":[792,795,796],"semantic_template":"qf-finite-set-difference/{\"A\":[791,792,794,796],\"B\":[792,795,796]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0021","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={801, 802, 804, 806}，B={802, 805, 806}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{801, 804}","explanation_zh":"801 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {805}，不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260985,"parameters":{"A":[801,802,804,806],"B":[802,805,806],"semantic_template":"qf-finite-set-difference/{\"A\":[801,802,804,806],\"B\":[802,805,806]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0022","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={811, 812, 814, 816}，B={812, 815, 816}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{811, 814}","explanation_zh":"811 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {815}，不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260986,"parameters":{"A":[811,812,814,816],"B":[812,815,816],"semantic_template":"qf-finite-set-difference/{\"A\":[811,812,814,816],\"B\":[812,815,816]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0023","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={821, 822, 824, 826}，B={822, 825, 826}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{821, 824}","explanation_zh":"821 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {825}，不可混同。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260987,"parameters":{"A":[821,822,824,826],"B":[822,825,826],"semantic_template":"qf-finite-set-difference/{\"A\":[821,822,824,826],\"B\":[822,825,826]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0024","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={831, 832, 834, 836}，B={832, 835, 836}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{831, 834}","explanation_zh":"831 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {835}，不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260988,"parameters":{"A":[831,832,834,836],"B":[832,835,836],"semantic_template":"qf-finite-set-difference/{\"A\":[831,832,834,836],\"B\":[832,835,836]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-set-difference-0025","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合方向性差集","stem_zh":"令 A={841, 842, 844, 846}，B={842, 845, 846}。求方向性差集 A\\B（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{841, 844}","explanation_zh":"841 屬於 A 而不屬於 B，所以保留於 A\\B；反向 B\\A 會是 {845}，不可混同。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合差集","運算方向"]},"variant":{"family_id":"qf-finite-set-difference","seed":20260989,"parameters":{"A":[841,842,844,846],"B":[842,845,846],"semantic_template":"qf-finite-set-difference/{\"A\":[841,842,844,846],\"B\":[842,845,846]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0001","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={901, 902, 903, 904, 905}，且 A={901, 903}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{902, 904, 905}","explanation_zh":"全集 U 已明示且 A⊆U；902 在 U 中但不在 A 中，所以 U\\A={902, 904, 905}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260990,"parameters":{"U":[901,902,903,904,905],"A":[901,903],"semantic_template":"qf-finite-relative-complement/{\"A\":[901,903],\"U\":[901,902,903,904,905]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0002","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={911, 912, 913, 914, 915}，且 A={912, 914, 915}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{911, 913}","explanation_zh":"全集 U 已明示且 A⊆U；911 在 U 中但不在 A 中，所以 U\\A={911, 913}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260991,"parameters":{"U":[911,912,913,914,915],"A":[912,914,915],"semantic_template":"qf-finite-relative-complement/{\"A\":[912,914,915],\"U\":[911,912,913,914,915]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0003","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={921, 922, 923, 924, 925}，且 A={921, 923}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{922, 924, 925}","explanation_zh":"全集 U 已明示且 A⊆U；922 在 U 中但不在 A 中，所以 U\\A={922, 924, 925}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260992,"parameters":{"U":[921,922,923,924,925],"A":[921,923],"semantic_template":"qf-finite-relative-complement/{\"A\":[921,923],\"U\":[921,922,923,924,925]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0004","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={931, 932, 933, 934, 935}，且 A={932, 934, 935}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{931, 933}","explanation_zh":"全集 U 已明示且 A⊆U；931 在 U 中但不在 A 中，所以 U\\A={931, 933}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260993,"parameters":{"U":[931,932,933,934,935],"A":[932,934,935],"semantic_template":"qf-finite-relative-complement/{\"A\":[932,934,935],\"U\":[931,932,933,934,935]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0005","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={941, 942, 943, 944, 945}，且 A={941, 943}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{942, 944, 945}","explanation_zh":"全集 U 已明示且 A⊆U；942 在 U 中但不在 A 中，所以 U\\A={942, 944, 945}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260994,"parameters":{"U":[941,942,943,944,945],"A":[941,943],"semantic_template":"qf-finite-relative-complement/{\"A\":[941,943],\"U\":[941,942,943,944,945]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0006","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={951, 952, 953, 954, 955}，且 A={952, 954, 955}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{951, 953}","explanation_zh":"全集 U 已明示且 A⊆U；951 在 U 中但不在 A 中，所以 U\\A={951, 953}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260995,"parameters":{"U":[951,952,953,954,955],"A":[952,954,955],"semantic_template":"qf-finite-relative-complement/{\"A\":[952,954,955],\"U\":[951,952,953,954,955]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0007","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={961, 962, 963, 964, 965}，且 A={961, 963}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{962, 964, 965}","explanation_zh":"全集 U 已明示且 A⊆U；962 在 U 中但不在 A 中，所以 U\\A={962, 964, 965}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260996,"parameters":{"U":[961,962,963,964,965],"A":[961,963],"semantic_template":"qf-finite-relative-complement/{\"A\":[961,963],\"U\":[961,962,963,964,965]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0008","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={971, 972, 973, 974, 975}，且 A={972, 974, 975}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{971, 973}","explanation_zh":"全集 U 已明示且 A⊆U；971 在 U 中但不在 A 中，所以 U\\A={971, 973}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260997,"parameters":{"U":[971,972,973,974,975],"A":[972,974,975],"semantic_template":"qf-finite-relative-complement/{\"A\":[972,974,975],\"U\":[971,972,973,974,975]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0009","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={981, 982, 983, 984, 985}，且 A={981, 983}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{982, 984, 985}","explanation_zh":"全集 U 已明示且 A⊆U；982 在 U 中但不在 A 中，所以 U\\A={982, 984, 985}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260998,"parameters":{"U":[981,982,983,984,985],"A":[981,983],"semantic_template":"qf-finite-relative-complement/{\"A\":[981,983],\"U\":[981,982,983,984,985]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0010","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={991, 992, 993, 994, 995}，且 A={992, 994, 995}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{991, 993}","explanation_zh":"全集 U 已明示且 A⊆U；991 在 U 中但不在 A 中，所以 U\\A={991, 993}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20260999,"parameters":{"U":[991,992,993,994,995],"A":[992,994,995],"semantic_template":"qf-finite-relative-complement/{\"A\":[992,994,995],\"U\":[991,992,993,994,995]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0011","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1001, 1002, 1003, 1004, 1005}，且 A={1001, 1003}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1002, 1004, 1005}","explanation_zh":"全集 U 已明示且 A⊆U；1002 在 U 中但不在 A 中，所以 U\\A={1002, 1004, 1005}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261000,"parameters":{"U":[1001,1002,1003,1004,1005],"A":[1001,1003],"semantic_template":"qf-finite-relative-complement/{\"A\":[1001,1003],\"U\":[1001,1002,1003,1004,1005]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0012","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1011, 1012, 1013, 1014, 1015}，且 A={1012, 1014, 1015}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1011, 1013}","explanation_zh":"全集 U 已明示且 A⊆U；1011 在 U 中但不在 A 中，所以 U\\A={1011, 1013}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261001,"parameters":{"U":[1011,1012,1013,1014,1015],"A":[1012,1014,1015],"semantic_template":"qf-finite-relative-complement/{\"A\":[1012,1014,1015],\"U\":[1011,1012,1013,1014,1015]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0013","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1021, 1022, 1023, 1024, 1025}，且 A={1021, 1023}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1022, 1024, 1025}","explanation_zh":"全集 U 已明示且 A⊆U；1022 在 U 中但不在 A 中，所以 U\\A={1022, 1024, 1025}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261002,"parameters":{"U":[1021,1022,1023,1024,1025],"A":[1021,1023],"semantic_template":"qf-finite-relative-complement/{\"A\":[1021,1023],\"U\":[1021,1022,1023,1024,1025]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0014","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1031, 1032, 1033, 1034, 1035}，且 A={1032, 1034, 1035}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1031, 1033}","explanation_zh":"全集 U 已明示且 A⊆U；1031 在 U 中但不在 A 中，所以 U\\A={1031, 1033}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261003,"parameters":{"U":[1031,1032,1033,1034,1035],"A":[1032,1034,1035],"semantic_template":"qf-finite-relative-complement/{\"A\":[1032,1034,1035],\"U\":[1031,1032,1033,1034,1035]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0015","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1041, 1042, 1043, 1044, 1045}，且 A={1041, 1043}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1042, 1044, 1045}","explanation_zh":"全集 U 已明示且 A⊆U；1042 在 U 中但不在 A 中，所以 U\\A={1042, 1044, 1045}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261004,"parameters":{"U":[1041,1042,1043,1044,1045],"A":[1041,1043],"semantic_template":"qf-finite-relative-complement/{\"A\":[1041,1043],\"U\":[1041,1042,1043,1044,1045]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0016","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1051, 1052, 1053, 1054, 1055}，且 A={1052, 1054, 1055}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1051, 1053}","explanation_zh":"全集 U 已明示且 A⊆U；1051 在 U 中但不在 A 中，所以 U\\A={1051, 1053}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261005,"parameters":{"U":[1051,1052,1053,1054,1055],"A":[1052,1054,1055],"semantic_template":"qf-finite-relative-complement/{\"A\":[1052,1054,1055],\"U\":[1051,1052,1053,1054,1055]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0017","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1061, 1062, 1063, 1064, 1065}，且 A={1061, 1063}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1062, 1064, 1065}","explanation_zh":"全集 U 已明示且 A⊆U；1062 在 U 中但不在 A 中，所以 U\\A={1062, 1064, 1065}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261006,"parameters":{"U":[1061,1062,1063,1064,1065],"A":[1061,1063],"semantic_template":"qf-finite-relative-complement/{\"A\":[1061,1063],\"U\":[1061,1062,1063,1064,1065]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0018","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1071, 1072, 1073, 1074, 1075}，且 A={1072, 1074, 1075}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1071, 1073}","explanation_zh":"全集 U 已明示且 A⊆U；1071 在 U 中但不在 A 中，所以 U\\A={1071, 1073}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261007,"parameters":{"U":[1071,1072,1073,1074,1075],"A":[1072,1074,1075],"semantic_template":"qf-finite-relative-complement/{\"A\":[1072,1074,1075],\"U\":[1071,1072,1073,1074,1075]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0019","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1081, 1082, 1083, 1084, 1085}，且 A={1081, 1083}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1082, 1084, 1085}","explanation_zh":"全集 U 已明示且 A⊆U；1082 在 U 中但不在 A 中，所以 U\\A={1082, 1084, 1085}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261008,"parameters":{"U":[1081,1082,1083,1084,1085],"A":[1081,1083],"semantic_template":"qf-finite-relative-complement/{\"A\":[1081,1083],\"U\":[1081,1082,1083,1084,1085]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0020","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1091, 1092, 1093, 1094, 1095}，且 A={1092, 1094, 1095}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1091, 1093}","explanation_zh":"全集 U 已明示且 A⊆U；1091 在 U 中但不在 A 中，所以 U\\A={1091, 1093}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261009,"parameters":{"U":[1091,1092,1093,1094,1095],"A":[1092,1094,1095],"semantic_template":"qf-finite-relative-complement/{\"A\":[1092,1094,1095],\"U\":[1091,1092,1093,1094,1095]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0021","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1101, 1102, 1103, 1104, 1105}，且 A={1101, 1103}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1102, 1104, 1105}","explanation_zh":"全集 U 已明示且 A⊆U；1102 在 U 中但不在 A 中，所以 U\\A={1102, 1104, 1105}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261010,"parameters":{"U":[1101,1102,1103,1104,1105],"A":[1101,1103],"semantic_template":"qf-finite-relative-complement/{\"A\":[1101,1103],\"U\":[1101,1102,1103,1104,1105]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0022","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1111, 1112, 1113, 1114, 1115}，且 A={1112, 1114, 1115}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1111, 1113}","explanation_zh":"全集 U 已明示且 A⊆U；1111 在 U 中但不在 A 中，所以 U\\A={1111, 1113}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261011,"parameters":{"U":[1111,1112,1113,1114,1115],"A":[1112,1114,1115],"semantic_template":"qf-finite-relative-complement/{\"A\":[1112,1114,1115],\"U\":[1111,1112,1113,1114,1115]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0023","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1121, 1122, 1123, 1124, 1125}，且 A={1121, 1123}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1122, 1124, 1125}","explanation_zh":"全集 U 已明示且 A⊆U；1122 在 U 中但不在 A 中，所以 U\\A={1122, 1124, 1125}。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261012,"parameters":{"U":[1121,1122,1123,1124,1125],"A":[1121,1123],"semantic_template":"qf-finite-relative-complement/{\"A\":[1121,1123],\"U\":[1121,1122,1123,1124,1125]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0024","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1131, 1132, 1133, 1134, 1135}，且 A={1132, 1134, 1135}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1131, 1133}","explanation_zh":"全集 U 已明示且 A⊆U；1131 在 U 中但不在 A 中，所以 U\\A={1131, 1133}。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261013,"parameters":{"U":[1131,1132,1133,1134,1135],"A":[1132,1134,1135],"semantic_template":"qf-finite-relative-complement/{\"A\":[1132,1134,1135],\"U\":[1131,1132,1133,1134,1135]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260915-finite-relative-complement-0025","batch_id":"batch-20260915-finite-set-operations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集的相對補集","stem_zh":"令明示全集 U={1141, 1142, 1143, 1144, 1145}，且 A={1141, 1143}⊆U。求相對補集 U\\A（元素只列一次並依遞增排序）。","answer":{"kind":"short_text","value":"{1142, 1144, 1145}","explanation_zh":"全集 U 已明示且 A⊆U；1142 在 U 中但不在 A 中，所以 U\\A={1142, 1144, 1145}。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["相對補集","全集"]},"variant":{"family_id":"qf-finite-relative-complement","seed":20261014,"parameters":{"U":[1141,1142,1143,1144,1145],"A":[1141,1143],"semantic_template":"qf-finite-relative-complement/{\"A\":[1141,1143],\"U\":[1141,1142,1143,1144,1145]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算明示有限集合的具體元素；不構成集合定理、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-15","contract_version":"ocme-question-factory-v0.1"}}