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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0016","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[0, 1]、B=[0, 1, 100, 101]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(4, 2)","explanation_zh":"聯交基數=(4, 2)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102016,"parameters":{"A":[0,1],"B":[0,1,100,101],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[0,2],2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0017","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[0]、B=[0, 100, 101, 102]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(4, 1)","explanation_zh":"聯交基數=(4, 1)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102017,"parameters":{"A":[0],"B":[0,100,101,102],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[0,3],1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0018","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[]、B=[100, 101, 102, 103]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(4, 0)","explanation_zh":"聯交基數=(4, 0)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102018,"parameters":{"A":[],"B":[100,101,102,103],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[0,4],0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0019","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[0, 1, -1]、B=[0, 1, 100]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(4, 2)","explanation_zh":"聯交基數=(4, 2)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102019,"parameters":{"A":[0,1,-1],"B":[0,1,100],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[1,1],2]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0020","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[0, -1]、B=[0, 100, 101]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(4, 1)","explanation_zh":"聯交基數=(4, 1)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102020,"parameters":{"A":[0,-1],"B":[0,100,101],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[1,2],1]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0021","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[-1]、B=[100, 101, 102]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(4, 0)","explanation_zh":"聯交基數=(4, 0)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102021,"parameters":{"A":[-1],"B":[100,101,102],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[1,3],0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0022","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[-2, -1]、B=[100, 101]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(4, 0)","explanation_zh":"聯交基數=(4, 0)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102022,"parameters":{"A":[-2,-1],"B":[100,101],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[2,2],0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0023","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[0, 1, 2, 3, 4]、B=[0, 1, 2, 3, 4]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(5, 5)","explanation_zh":"聯交基數=(5, 5)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102023,"parameters":{"A":[0,1,2,3,4],"B":[0,1,2,3,4],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[0,0],5]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0024","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[0, 1, 2, 3]、B=[0, 1, 2, 3, 100]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(5, 4)","explanation_zh":"聯交基數=(5, 4)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102024,"parameters":{"A":[0,1,2,3],"B":[0,1,2,3,100],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[0,1],4]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0025","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"有限集合聯交的基數對","stem_zh":"有限整數集合 A=[0, 1, 2]、B=[0, 1, 2, 100, 101]。依序求 (|A∪B|, |A∩B|)，重列元素只算一次。","answer":{"kind":"expression","value":"(5, 3)","explanation_zh":"聯交基數=(5, 3)。依隸屬逐元素計數；交集元素在聯集只算一次，空集大小為零。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限集合聯交的基數對"]},"variant":{"family_id":"qf-density10-set-union-intersection-sizes","seed":202610102025,"parameters":{"A":[0,1,2],"B":[0,1,2,100,101],"operation":"density10_set_union_intersection_sizes","domain":"finite_integer_sets","semantic_template":"qf-density10-set-union-intersection-sizes/[[0,2],3]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0026","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[]、B=[]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[]","explanation_zh":"兩側差聯集=[]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102026,"parameters":{"A":[],"B":[],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0027","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[0, 1]、B=[0, 1]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[]","explanation_zh":"兩側差聯集=[]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102027,"parameters":{"A":[0,1],"B":[0,1],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[0,1],[0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0028","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[]、B=[-2, 2]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-2, 2]","explanation_zh":"兩側差聯集=[-2, 2]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102028,"parameters":{"A":[],"B":[-2,2],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-2,2],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0029","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-3, 0, 3]、B=[0, 4]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-3, 3, 4]","explanation_zh":"兩側差聯集=[-3, 3, 4]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102029,"parameters":{"A":[-3,0,3],"B":[0,4],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-3,0,3],[0,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0030","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-4, 0, 4]、B=[0, 5]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-4, 4, 5]","explanation_zh":"兩側差聯集=[-4, 4, 5]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102030,"parameters":{"A":[-4,0,4],"B":[0,5],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-4,0,4],[0,5]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0031","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-5, 0, 5]、B=[0, 6]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-5, 5, 6]","explanation_zh":"兩側差聯集=[-5, 5, 6]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102031,"parameters":{"A":[-5,0,5],"B":[0,6],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-5,0,5],[0,6]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0032","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-6, 0, 6]、B=[0, 7]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-6, 6, 7]","explanation_zh":"兩側差聯集=[-6, 6, 7]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102032,"parameters":{"A":[-6,0,6],"B":[0,7],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-6,0,6],[0,7]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0033","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-7, 0, 7]、B=[0, 8]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-7, 7, 8]","explanation_zh":"兩側差聯集=[-7, 7, 8]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102033,"parameters":{"A":[-7,0,7],"B":[0,8],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-7,0,7],[0,8]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0034","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-8, 0, 8]、B=[0, 9]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-8, 8, 9]","explanation_zh":"兩側差聯集=[-8, 8, 9]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102034,"parameters":{"A":[-8,0,8],"B":[0,9],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-8,0,8],[0,9]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0035","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-9, 0, 9]、B=[0, 10]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-9, 9, 10]","explanation_zh":"兩側差聯集=[-9, 9, 10]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102035,"parameters":{"A":[-9,0,9],"B":[0,10],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-9,0,9],[0,10]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0036","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-10, 0, 10]、B=[0, 11]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-10, 10, 11]","explanation_zh":"兩側差聯集=[-10, 10, 11]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102036,"parameters":{"A":[-10,0,10],"B":[0,11],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-10,0,10],[0,11]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0037","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-11, 0, 11]、B=[0, 12]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-11, 11, 12]","explanation_zh":"兩側差聯集=[-11, 11, 12]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102037,"parameters":{"A":[-11,0,11],"B":[0,12],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-11,0,11],[0,12]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0038","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-12, 0, 12]、B=[0, 13]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-12, 12, 13]","explanation_zh":"兩側差聯集=[-12, 12, 13]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102038,"parameters":{"A":[-12,0,12],"B":[0,13],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-12,0,12],[0,13]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0039","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-13, 0, 13]、B=[0, 14]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-13, 13, 14]","explanation_zh":"兩側差聯集=[-13, 13, 14]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102039,"parameters":{"A":[-13,0,13],"B":[0,14],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-13,0,13],[0,14]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0040","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-14, 0, 14]、B=[0, 15]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-14, 14, 15]","explanation_zh":"兩側差聯集=[-14, 14, 15]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102040,"parameters":{"A":[-14,0,14],"B":[0,15],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-14,0,14],[0,15]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0041","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-15, 0, 15]、B=[0, 16]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-15, 15, 16]","explanation_zh":"兩側差聯集=[-15, 15, 16]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102041,"parameters":{"A":[-15,0,15],"B":[0,16],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-15,0,15],[0,16]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0042","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-16, 0, 16]、B=[0, 17]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-16, 16, 17]","explanation_zh":"兩側差聯集=[-16, 16, 17]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102042,"parameters":{"A":[-16,0,16],"B":[0,17],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-16,0,16],[0,17]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0043","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-17, 0, 17]、B=[0, 18]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-17, 17, 18]","explanation_zh":"兩側差聯集=[-17, 17, 18]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102043,"parameters":{"A":[-17,0,17],"B":[0,18],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-17,0,17],[0,18]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0044","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-18, 0, 18]、B=[0, 19]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-18, 18, 19]","explanation_zh":"兩側差聯集=[-18, 18, 19]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102044,"parameters":{"A":[-18,0,18],"B":[0,19],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-18,0,18],[0,19]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0045","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-19, 0, 19]、B=[0, 20]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-19, 19, 20]","explanation_zh":"兩側差聯集=[-19, 19, 20]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102045,"parameters":{"A":[-19,0,19],"B":[0,20],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-19,0,19],[0,20]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0046","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-20, 0, 20]、B=[0, 21]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-20, 20, 21]","explanation_zh":"兩側差聯集=[-20, 20, 21]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102046,"parameters":{"A":[-20,0,20],"B":[0,21],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-20,0,20],[0,21]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0047","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-21, 0, 21]、B=[0, 22]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-21, 21, 22]","explanation_zh":"兩側差聯集=[-21, 21, 22]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102047,"parameters":{"A":[-21,0,21],"B":[0,22],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-21,0,21],[0,22]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0048","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-22, 0, 22]、B=[0, 23]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-22, 22, 23]","explanation_zh":"兩側差聯集=[-22, 22, 23]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102048,"parameters":{"A":[-22,0,22],"B":[0,23],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-22,0,22],[0,23]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0049","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-23, 0, 23]、B=[0, 24]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-23, 23, 24]","explanation_zh":"兩側差聯集=[-23, 23, 24]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102049,"parameters":{"A":[-23,0,23],"B":[0,24],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-23,0,23],[0,24]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0050","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"兩側差的聯集","stem_zh":"有限整數集合 A=[-24, 0, 24]、B=[0, 25]。列 (A\\B)∪(B\\A)，按整數遞增且不重列。","answer":{"kind":"expression","value":"[-24, 24, 25]","explanation_zh":"兩側差聯集=[-24, 24, 25]。保留僅屬一側的元素；兩側都屬的元素排除，並非一般聯集。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["兩側差的聯集"]},"variant":{"family_id":"qf-density10-set-symmetric-difference","seed":202610102050,"parameters":{"A":[-24,0,24],"B":[0,25],"operation":"density10_set_symmetric_difference","domain":"finite_integer_sets","semantic_template":"qf-density10-set-symmetric-difference/[[-24,0,24],[0,25]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0051","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[]、A=[]、B=[]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([], [])","explanation_zh":"補集兩式=([], [])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102051,"parameters":{"U":[],"A":[],"B":[],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0052","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-1, 0, 1]、A=[-1, 0]、B=[1]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([], [])","explanation_zh":"補集兩式=([], [])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102052,"parameters":{"U":[-1,0,1],"A":[-1,0],"B":[1],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-1,0,1],[-1,0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0053","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-2, -1, 0, 1, 2]、A=[0]、B=[-1, 2]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-2, 1], [-2, 1])","explanation_zh":"補集兩式=([-2, 1], [-2, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102053,"parameters":{"U":[-2,-1,0,1,2],"A":[0],"B":[-1,2],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-2,-1,0,1,2],[-1,0,2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0054","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-3, -1, 0, 1, 3]、A=[0]、B=[-1, 3]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-3, 1], [-3, 1])","explanation_zh":"補集兩式=([-3, 1], [-3, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102054,"parameters":{"U":[-3,-1,0,1,3],"A":[0],"B":[-1,3],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-3,-1,0,1,3],[-1,0,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0055","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-4, -1, 0, 1, 4]、A=[0]、B=[-1, 4]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-4, 1], [-4, 1])","explanation_zh":"補集兩式=([-4, 1], [-4, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102055,"parameters":{"U":[-4,-1,0,1,4],"A":[0],"B":[-1,4],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-4,-1,0,1,4],[-1,0,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0056","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-5, -1, 0, 1, 5]、A=[0]、B=[-1, 5]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-5, 1], [-5, 1])","explanation_zh":"補集兩式=([-5, 1], [-5, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102056,"parameters":{"U":[-5,-1,0,1,5],"A":[0],"B":[-1,5],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-5,-1,0,1,5],[-1,0,5]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0057","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-6, -1, 0, 1, 6]、A=[0]、B=[-1, 6]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-6, 1], [-6, 1])","explanation_zh":"補集兩式=([-6, 1], [-6, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102057,"parameters":{"U":[-6,-1,0,1,6],"A":[0],"B":[-1,6],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-6,-1,0,1,6],[-1,0,6]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0058","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-7, -1, 0, 1, 7]、A=[0]、B=[-1, 7]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-7, 1], [-7, 1])","explanation_zh":"補集兩式=([-7, 1], [-7, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102058,"parameters":{"U":[-7,-1,0,1,7],"A":[0],"B":[-1,7],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-7,-1,0,1,7],[-1,0,7]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0059","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-8, -1, 0, 1, 8]、A=[0]、B=[-1, 8]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-8, 1], [-8, 1])","explanation_zh":"補集兩式=([-8, 1], [-8, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102059,"parameters":{"U":[-8,-1,0,1,8],"A":[0],"B":[-1,8],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-8,-1,0,1,8],[-1,0,8]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0060","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-9, -1, 0, 1, 9]、A=[0]、B=[-1, 9]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-9, 1], [-9, 1])","explanation_zh":"補集兩式=([-9, 1], [-9, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102060,"parameters":{"U":[-9,-1,0,1,9],"A":[0],"B":[-1,9],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-9,-1,0,1,9],[-1,0,9]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0061","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-10, -1, 0, 1, 10]、A=[0]、B=[-1, 10]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-10, 1], [-10, 1])","explanation_zh":"補集兩式=([-10, 1], [-10, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102061,"parameters":{"U":[-10,-1,0,1,10],"A":[0],"B":[-1,10],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-10,-1,0,1,10],[-1,0,10]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0062","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-11, -1, 0, 1, 11]、A=[0]、B=[-1, 11]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-11, 1], [-11, 1])","explanation_zh":"補集兩式=([-11, 1], [-11, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102062,"parameters":{"U":[-11,-1,0,1,11],"A":[0],"B":[-1,11],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-11,-1,0,1,11],[-1,0,11]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0063","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-12, -1, 0, 1, 12]、A=[0]、B=[-1, 12]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-12, 1], [-12, 1])","explanation_zh":"補集兩式=([-12, 1], [-12, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102063,"parameters":{"U":[-12,-1,0,1,12],"A":[0],"B":[-1,12],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-12,-1,0,1,12],[-1,0,12]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0064","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-13, -1, 0, 1, 13]、A=[0]、B=[-1, 13]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-13, 1], [-13, 1])","explanation_zh":"補集兩式=([-13, 1], [-13, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102064,"parameters":{"U":[-13,-1,0,1,13],"A":[0],"B":[-1,13],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-13,-1,0,1,13],[-1,0,13]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0065","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-14, -1, 0, 1, 14]、A=[0]、B=[-1, 14]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-14, 1], [-14, 1])","explanation_zh":"補集兩式=([-14, 1], [-14, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102065,"parameters":{"U":[-14,-1,0,1,14],"A":[0],"B":[-1,14],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-14,-1,0,1,14],[-1,0,14]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0066","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-15, -1, 0, 1, 15]、A=[0]、B=[-1, 15]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-15, 1], [-15, 1])","explanation_zh":"補集兩式=([-15, 1], [-15, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102066,"parameters":{"U":[-15,-1,0,1,15],"A":[0],"B":[-1,15],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-15,-1,0,1,15],[-1,0,15]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0067","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-16, -1, 0, 1, 16]、A=[0]、B=[-1, 16]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-16, 1], [-16, 1])","explanation_zh":"補集兩式=([-16, 1], [-16, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102067,"parameters":{"U":[-16,-1,0,1,16],"A":[0],"B":[-1,16],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-16,-1,0,1,16],[-1,0,16]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0068","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-17, -1, 0, 1, 17]、A=[0]、B=[-1, 17]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-17, 1], [-17, 1])","explanation_zh":"補集兩式=([-17, 1], [-17, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102068,"parameters":{"U":[-17,-1,0,1,17],"A":[0],"B":[-1,17],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-17,-1,0,1,17],[-1,0,17]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0069","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-18, -1, 0, 1, 18]、A=[0]、B=[-1, 18]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-18, 1], [-18, 1])","explanation_zh":"補集兩式=([-18, 1], [-18, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102069,"parameters":{"U":[-18,-1,0,1,18],"A":[0],"B":[-1,18],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-18,-1,0,1,18],[-1,0,18]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0070","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-19, -1, 0, 1, 19]、A=[0]、B=[-1, 19]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-19, 1], [-19, 1])","explanation_zh":"補集兩式=([-19, 1], [-19, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102070,"parameters":{"U":[-19,-1,0,1,19],"A":[0],"B":[-1,19],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-19,-1,0,1,19],[-1,0,19]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0071","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-20, -1, 0, 1, 20]、A=[0]、B=[-1, 20]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-20, 1], [-20, 1])","explanation_zh":"補集兩式=([-20, 1], [-20, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102071,"parameters":{"U":[-20,-1,0,1,20],"A":[0],"B":[-1,20],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-20,-1,0,1,20],[-1,0,20]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0072","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-21, -1, 0, 1, 21]、A=[0]、B=[-1, 21]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-21, 1], [-21, 1])","explanation_zh":"補集兩式=([-21, 1], [-21, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102072,"parameters":{"U":[-21,-1,0,1,21],"A":[0],"B":[-1,21],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-21,-1,0,1,21],[-1,0,21]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0073","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-22, -1, 0, 1, 22]、A=[0]、B=[-1, 22]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-22, 1], [-22, 1])","explanation_zh":"補集兩式=([-22, 1], [-22, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102073,"parameters":{"U":[-22,-1,0,1,22],"A":[0],"B":[-1,22],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-22,-1,0,1,22],[-1,0,22]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0074","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-23, -1, 0, 1, 23]、A=[0]、B=[-1, 23]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-23, 1], [-23, 1])","explanation_zh":"補集兩式=([-23, 1], [-23, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102074,"parameters":{"U":[-23,-1,0,1,23],"A":[0],"B":[-1,23],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-23,-1,0,1,23],[-1,0,23]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0075","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"明示全集下的兩個補集式","stem_zh":"有限整數集合，全集U=[-24, -1, 0, 1, 24]、A=[0]、B=[-1, 24]，A、B⊆U。依序列 (U\\(A∪B), (U\\A)∩(U\\B))，各列遞增。","answer":{"kind":"expression","value":"([-24, 1], [-24, 1])","explanation_zh":"補集兩式=([-24, 1], [-24, 1])。第一式找U內兩側皆不屬者，第二式分別取補後交集；補集只相對明示U。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["明示全集下的兩個補集式"]},"variant":{"family_id":"qf-density10-set-demorgan-sets","seed":202610102075,"parameters":{"U":[-24,-1,0,1,24],"A":[0],"B":[-1,24],"operation":"density10_set_demorgan_sets","domain":"finite_integer_sets","semantic_template":"qf-density10-set-demorgan-sets/[[-24,-1,0,1,24],[-1,0,24]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0076","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[]、B=[]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([], [], [])","explanation_zh":"有序三段分割=([], [], [])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102076,"parameters":{"A":[],"B":[],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[],[]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0077","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-1, 0]、B=[0, 1]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-1], [0], [1])","explanation_zh":"有序三段分割=([-1], [0], [1])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102077,"parameters":{"A":[-1,0],"B":[0,1],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-1,0],[0,1]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0078","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-2, 0, 2]、B=[0, 2, 3]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-2], [0, 2], [3])","explanation_zh":"有序三段分割=([-2], [0, 2], [3])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102078,"parameters":{"A":[-2,0,2],"B":[0,2,3],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-2,0,2],[0,2,3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0079","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-3, 0, 3]、B=[0, 3, 4]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-3], [0, 3], [4])","explanation_zh":"有序三段分割=([-3], [0, 3], [4])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102079,"parameters":{"A":[-3,0,3],"B":[0,3,4],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-3,0,3],[0,3,4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0080","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-4, 0, 4]、B=[0, 4, 5]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-4], [0, 4], [5])","explanation_zh":"有序三段分割=([-4], [0, 4], [5])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102080,"parameters":{"A":[-4,0,4],"B":[0,4,5],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-4,0,4],[0,4,5]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0081","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-5, 0, 5]、B=[0, 5, 6]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-5], [0, 5], [6])","explanation_zh":"有序三段分割=([-5], [0, 5], [6])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102081,"parameters":{"A":[-5,0,5],"B":[0,5,6],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-5,0,5],[0,5,6]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0082","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-6, 0, 6]、B=[0, 6, 7]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-6], [0, 6], [7])","explanation_zh":"有序三段分割=([-6], [0, 6], [7])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102082,"parameters":{"A":[-6,0,6],"B":[0,6,7],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-6,0,6],[0,6,7]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0083","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-7, 0, 7]、B=[0, 7, 8]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-7], [0, 7], [8])","explanation_zh":"有序三段分割=([-7], [0, 7], [8])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102083,"parameters":{"A":[-7,0,7],"B":[0,7,8],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-7,0,7],[0,7,8]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0084","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-8, 0, 8]、B=[0, 8, 9]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-8], [0, 8], [9])","explanation_zh":"有序三段分割=([-8], [0, 8], [9])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102084,"parameters":{"A":[-8,0,8],"B":[0,8,9],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-8,0,8],[0,8,9]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0085","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-9, 0, 9]、B=[0, 9, 10]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-9], [0, 9], [10])","explanation_zh":"有序三段分割=([-9], [0, 9], [10])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102085,"parameters":{"A":[-9,0,9],"B":[0,9,10],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-9,0,9],[0,9,10]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0086","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-10, 0, 10]、B=[0, 10, 11]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-10], [0, 10], [11])","explanation_zh":"有序三段分割=([-10], [0, 10], [11])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102086,"parameters":{"A":[-10,0,10],"B":[0,10,11],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-10,0,10],[0,10,11]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0087","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-11, 0, 11]、B=[0, 11, 12]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-11], [0, 11], [12])","explanation_zh":"有序三段分割=([-11], [0, 11], [12])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102087,"parameters":{"A":[-11,0,11],"B":[0,11,12],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-11,0,11],[0,11,12]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0088","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-12, 0, 12]、B=[0, 12, 13]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-12], [0, 12], [13])","explanation_zh":"有序三段分割=([-12], [0, 12], [13])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102088,"parameters":{"A":[-12,0,12],"B":[0,12,13],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-12,0,12],[0,12,13]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0089","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-13, 0, 13]、B=[0, 13, 14]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-13], [0, 13], [14])","explanation_zh":"有序三段分割=([-13], [0, 13], [14])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102089,"parameters":{"A":[-13,0,13],"B":[0,13,14],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-13,0,13],[0,13,14]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0090","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-14, 0, 14]、B=[0, 14, 15]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-14], [0, 14], [15])","explanation_zh":"有序三段分割=([-14], [0, 14], [15])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102090,"parameters":{"A":[-14,0,14],"B":[0,14,15],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-14,0,14],[0,14,15]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0091","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-15, 0, 15]、B=[0, 15, 16]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-15], [0, 15], [16])","explanation_zh":"有序三段分割=([-15], [0, 15], [16])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102091,"parameters":{"A":[-15,0,15],"B":[0,15,16],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-15,0,15],[0,15,16]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0092","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-16, 0, 16]、B=[0, 16, 17]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-16], [0, 16], [17])","explanation_zh":"有序三段分割=([-16], [0, 16], [17])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102092,"parameters":{"A":[-16,0,16],"B":[0,16,17],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-16,0,16],[0,16,17]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0093","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-17, 0, 17]、B=[0, 17, 18]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-17], [0, 17], [18])","explanation_zh":"有序三段分割=([-17], [0, 17], [18])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102093,"parameters":{"A":[-17,0,17],"B":[0,17,18],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-17,0,17],[0,17,18]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0094","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-18, 0, 18]、B=[0, 18, 19]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-18], [0, 18], [19])","explanation_zh":"有序三段分割=([-18], [0, 18], [19])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102094,"parameters":{"A":[-18,0,18],"B":[0,18,19],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-18,0,18],[0,18,19]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0095","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-19, 0, 19]、B=[0, 19, 20]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-19], [0, 19], [20])","explanation_zh":"有序三段分割=([-19], [0, 19], [20])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102095,"parameters":{"A":[-19,0,19],"B":[0,19,20],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-19,0,19],[0,19,20]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0096","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-20, 0, 20]、B=[0, 20, 21]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-20], [0, 20], [21])","explanation_zh":"有序三段分割=([-20], [0, 20], [21])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102096,"parameters":{"A":[-20,0,20],"B":[0,20,21],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-20,0,20],[0,20,21]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0097","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-21, 0, 21]、B=[0, 21, 22]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-21], [0, 21], [22])","explanation_zh":"有序三段分割=([-21], [0, 21], [22])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102097,"parameters":{"A":[-21,0,21],"B":[0,21,22],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-21,0,21],[0,21,22]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0098","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-22, 0, 22]、B=[0, 22, 23]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-22], [0, 22], [23])","explanation_zh":"有序三段分割=([-22], [0, 22], [23])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102098,"parameters":{"A":[-22,0,22],"B":[0,22,23],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-22,0,22],[0,22,23]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261010-r02-set-operations-0100","batch_id":"batch-20261008-advance-20261010-r02-set-operations-foundations","language":"zh-Hant","source_mko_ids":["mko-set-operations"],"title_zh":"集合的有序三段分割","stem_zh":"有限整數集合 A=[-24, 0, 24]、B=[0, 24, 25]。依序列 (A\\B, A∩B, B\\A)，各段遞增，保留空段。","answer":{"kind":"expression","value":"([-24], [0, 24], [25])","explanation_zh":"有序三段分割=([-24], [0, 24], [25])。逐元素按兩側隸屬分到三段；次序是左獨有、共有、右獨有，不交換兩側。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["集合的有序三段分割"]},"variant":{"family_id":"qf-density10-set-three-way-partition","seed":202610102100,"parameters":{"A":[-24,0,24],"B":[0,24,25],"operation":"density10_set_three_way_partition","domain":"finite_integer_sets","semantic_template":"qf-density10-set-three-way-partition/[[-24,0,24],[0,24,25]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}