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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r04-set-0027","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[]、B=[-1]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [], [-1])","explanation_zh":"相等資格與雙向差=(否, [], [-1])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114027,"parameters":{"A":[],"B":[-1],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[],[-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-20261011-r04-set-0028","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-2]、B=[]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-2], [])","explanation_zh":"相等資格與雙向差=(否, [-2], [])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114028,"parameters":{"A":[-2],"B":[],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0029","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-3, 0, 3]、B=[0, 3, 4]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-3], [4])","explanation_zh":"相等資格與雙向差=(否, [-3], [4])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114029,"parameters":{"A":[-3,0,3],"B":[0,3,4],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0030","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-4, 0, 4]、B=[0, 4, 5]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-4], [5])","explanation_zh":"相等資格與雙向差=(否, [-4], [5])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114030,"parameters":{"A":[-4,0,4],"B":[0,4,5],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0031","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-5, 0, 5]、B=[0, 5, 6]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-5], [6])","explanation_zh":"相等資格與雙向差=(否, [-5], [6])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114031,"parameters":{"A":[-5,0,5],"B":[0,5,6],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0032","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-6, 0, 6]、B=[0, 6, 7]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-6], [7])","explanation_zh":"相等資格與雙向差=(否, [-6], [7])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114032,"parameters":{"A":[-6,0,6],"B":[0,6,7],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0033","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-7, 0, 7]、B=[0, 7, 8]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-7], [8])","explanation_zh":"相等資格與雙向差=(否, [-7], [8])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114033,"parameters":{"A":[-7,0,7],"B":[0,7,8],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0034","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-8, 0, 8]、B=[0, 8, 9]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-8], [9])","explanation_zh":"相等資格與雙向差=(否, [-8], [9])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114034,"parameters":{"A":[-8,0,8],"B":[0,8,9],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0035","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-9, 0, 9]、B=[0, 9, 10]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-9], [10])","explanation_zh":"相等資格與雙向差=(否, [-9], [10])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114035,"parameters":{"A":[-9,0,9],"B":[0,9,10],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0036","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-10, 0, 10]、B=[0, 10, 11]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-10], [11])","explanation_zh":"相等資格與雙向差=(否, [-10], [11])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114036,"parameters":{"A":[-10,0,10],"B":[0,10,11],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0037","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-11, 0, 11]、B=[0, 11, 12]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-11], [12])","explanation_zh":"相等資格與雙向差=(否, [-11], [12])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114037,"parameters":{"A":[-11,0,11],"B":[0,11,12],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0038","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-12, 0, 12]、B=[0, 12, 13]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-12], [13])","explanation_zh":"相等資格與雙向差=(否, [-12], [13])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114038,"parameters":{"A":[-12,0,12],"B":[0,12,13],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0039","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-13, 0, 13]、B=[0, 13, 14]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-13], [14])","explanation_zh":"相等資格與雙向差=(否, [-13], [14])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114039,"parameters":{"A":[-13,0,13],"B":[0,13,14],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0040","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-14, 0, 14]、B=[0, 14, 15]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-14], [15])","explanation_zh":"相等資格與雙向差=(否, [-14], [15])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114040,"parameters":{"A":[-14,0,14],"B":[0,14,15],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0041","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-15, 0, 15]、B=[0, 15, 16]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-15], [16])","explanation_zh":"相等資格與雙向差=(否, [-15], [16])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114041,"parameters":{"A":[-15,0,15],"B":[0,15,16],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0042","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-16, 0, 16]、B=[0, 16, 17]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-16], [17])","explanation_zh":"相等資格與雙向差=(否, [-16], [17])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114042,"parameters":{"A":[-16,0,16],"B":[0,16,17],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0043","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-17, 0, 17]、B=[0, 17, 18]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-17], [18])","explanation_zh":"相等資格與雙向差=(否, [-17], [18])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114043,"parameters":{"A":[-17,0,17],"B":[0,17,18],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0044","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-18, 0, 18]、B=[0, 18, 19]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-18], [19])","explanation_zh":"相等資格與雙向差=(否, [-18], [19])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114044,"parameters":{"A":[-18,0,18],"B":[0,18,19],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0045","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-19, 0, 19]、B=[0, 19, 20]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-19], [20])","explanation_zh":"相等資格與雙向差=(否, [-19], [20])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114045,"parameters":{"A":[-19,0,19],"B":[0,19,20],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0046","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-20, 0, 20]、B=[0, 20, 21]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-20], [21])","explanation_zh":"相等資格與雙向差=(否, [-20], [21])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114046,"parameters":{"A":[-20,0,20],"B":[0,20,21],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0047","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-21, 0, 21]、B=[0, 21, 22]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-21], [22])","explanation_zh":"相等資格與雙向差=(否, [-21], [22])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114047,"parameters":{"A":[-21,0,21],"B":[0,21,22],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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-20261011-r04-set-0048","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-22, 0, 22]、B=[0, 22, 23]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-22], [23])","explanation_zh":"相等資格與雙向差=(否, [-22], [23])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114048,"parameters":{"A":[-22,0,22],"B":[0,22,23],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r04-set-0049","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-23, 0, 23]、B=[0, 23, 24]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-23], [24])","explanation_zh":"相等資格與雙向差=(否, [-23], [24])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114049,"parameters":{"A":[-23,0,23],"B":[0,23,24],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-23],[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-20261011-r04-set-0050","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"集合相等與雙向差","stem_zh":"有限整數集合；A=[-24, 0, 24]、B=[0, 24, 25]。依序答 (A與B是否相等, A\\B, B\\A)，差集遞增列舉。","answer":{"kind":"expression","value":"(否, [-24], [25])","explanation_zh":"相等資格與雙向差=(否, [-24], [25])。先逐元素取兩側差；兩側差都空才相等，只看大小相同不足。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["集合相等與雙向差"]},"variant":{"family_id":"qf-density11-set-equality-defect","seed":202610114050,"parameters":{"A":[-24,0,24],"B":[0,24,25],"operation":"density11_set_equality_defect","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-equality-defect/[[-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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r04-set-0051","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[]、候選原列=[]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([], [])","explanation_zh":"候選元素分割=([], [])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114051,"parameters":{"A":[],"candidates":[],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-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-20261011-r04-set-0052","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[0]、候選原列=[0, 1, 1]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([0], [1])","explanation_zh":"候選元素分割=([0], [1])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114052,"parameters":{"A":[0],"candidates":[0,1,1],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[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-20261011-r04-set-0053","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-2, 0]、候選原列=[-2, 2, 0, 2]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-2, 0], [2])","explanation_zh":"候選元素分割=([-2, 0], [2])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114053,"parameters":{"A":[-2,0],"candidates":[-2,2,0,2],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-2,0],[2]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r04-set-0054","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-3, 0]、候選原列=[-3, 3, 0, 3]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-3, 0], [3])","explanation_zh":"候選元素分割=([-3, 0], [3])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114054,"parameters":{"A":[-3,0],"candidates":[-3,3,0,3],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-3,0],[3]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r04-set-0055","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-4, 0]、候選原列=[-4, 4, 0, 4]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-4, 0], [4])","explanation_zh":"候選元素分割=([-4, 0], [4])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114055,"parameters":{"A":[-4,0],"candidates":[-4,4,0,4],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-4,0],[4]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r04-set-0056","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-5, 0]、候選原列=[-5, 5, 0, 5]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-5, 0], [5])","explanation_zh":"候選元素分割=([-5, 0], [5])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114056,"parameters":{"A":[-5,0],"candidates":[-5,5,0,5],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-5,0],[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-20261011-r04-set-0057","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-6, 0]、候選原列=[-6, 6, 0, 6]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-6, 0], [6])","explanation_zh":"候選元素分割=([-6, 0], [6])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114057,"parameters":{"A":[-6,0],"candidates":[-6,6,0,6],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-6,0],[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-20261011-r04-set-0058","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-7, 0]、候選原列=[-7, 7, 0, 7]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-7, 0], [7])","explanation_zh":"候選元素分割=([-7, 0], [7])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114058,"parameters":{"A":[-7,0],"candidates":[-7,7,0,7],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-7,0],[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-20261011-r04-set-0059","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-8, 0]、候選原列=[-8, 8, 0, 8]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-8, 0], [8])","explanation_zh":"候選元素分割=([-8, 0], [8])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114059,"parameters":{"A":[-8,0],"candidates":[-8,8,0,8],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-8,0],[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-20261011-r04-set-0060","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-9, 0]、候選原列=[-9, 9, 0, 9]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-9, 0], [9])","explanation_zh":"候選元素分割=([-9, 0], [9])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114060,"parameters":{"A":[-9,0],"candidates":[-9,9,0,9],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-9,0],[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-20261011-r04-set-0061","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-10, 0]、候選原列=[-10, 10, 0, 10]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-10, 0], [10])","explanation_zh":"候選元素分割=([-10, 0], [10])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114061,"parameters":{"A":[-10,0],"candidates":[-10,10,0,10],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-10,0],[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-20261011-r04-set-0062","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-11, 0]、候選原列=[-11, 11, 0, 11]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-11, 0], [11])","explanation_zh":"候選元素分割=([-11, 0], [11])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114062,"parameters":{"A":[-11,0],"candidates":[-11,11,0,11],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-11,0],[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-20261011-r04-set-0063","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-12, 0]、候選原列=[-12, 12, 0, 12]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-12, 0], [12])","explanation_zh":"候選元素分割=([-12, 0], [12])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114063,"parameters":{"A":[-12,0],"candidates":[-12,12,0,12],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-12,0],[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-20261011-r04-set-0064","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-13, 0]、候選原列=[-13, 13, 0, 13]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-13, 0], [13])","explanation_zh":"候選元素分割=([-13, 0], [13])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114064,"parameters":{"A":[-13,0],"candidates":[-13,13,0,13],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-13,0],[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-20261011-r04-set-0065","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-14, 0]、候選原列=[-14, 14, 0, 14]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-14, 0], [14])","explanation_zh":"候選元素分割=([-14, 0], [14])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114065,"parameters":{"A":[-14,0],"candidates":[-14,14,0,14],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-14,0],[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-20261011-r04-set-0066","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-15, 0]、候選原列=[-15, 15, 0, 15]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-15, 0], [15])","explanation_zh":"候選元素分割=([-15, 0], [15])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114066,"parameters":{"A":[-15,0],"candidates":[-15,15,0,15],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-15,0],[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-20261011-r04-set-0067","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-16, 0]、候選原列=[-16, 16, 0, 16]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-16, 0], [16])","explanation_zh":"候選元素分割=([-16, 0], [16])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114067,"parameters":{"A":[-16,0],"candidates":[-16,16,0,16],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-16,0],[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-20261011-r04-set-0068","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-17, 0]、候選原列=[-17, 17, 0, 17]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-17, 0], [17])","explanation_zh":"候選元素分割=([-17, 0], [17])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114068,"parameters":{"A":[-17,0],"candidates":[-17,17,0,17],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-17,0],[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-20261011-r04-set-0069","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-18, 0]、候選原列=[-18, 18, 0, 18]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-18, 0], [18])","explanation_zh":"候選元素分割=([-18, 0], [18])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114069,"parameters":{"A":[-18,0],"candidates":[-18,18,0,18],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-18,0],[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-20261011-r04-set-0070","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-19, 0]、候選原列=[-19, 19, 0, 19]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-19, 0], [19])","explanation_zh":"候選元素分割=([-19, 0], [19])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114070,"parameters":{"A":[-19,0],"candidates":[-19,19,0,19],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-19,0],[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-20261011-r04-set-0071","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-20, 0]、候選原列=[-20, 20, 0, 20]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-20, 0], [20])","explanation_zh":"候選元素分割=([-20, 0], [20])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114071,"parameters":{"A":[-20,0],"candidates":[-20,20,0,20],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-20,0],[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-20261011-r04-set-0072","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-21, 0]、候選原列=[-21, 21, 0, 21]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-21, 0], [21])","explanation_zh":"候選元素分割=([-21, 0], [21])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114072,"parameters":{"A":[-21,0],"candidates":[-21,21,0,21],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-21,0],[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-20261011-r04-set-0073","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-22, 0]、候選原列=[-22, 22, 0, 22]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-22, 0], [22])","explanation_zh":"候選元素分割=([-22, 0], [22])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114073,"parameters":{"A":[-22,0],"candidates":[-22,22,0,22],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-22,0],[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-20261011-r04-set-0074","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-23, 0]、候選原列=[-23, 23, 0, 23]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-23, 0], [23])","explanation_zh":"候選元素分割=([-23, 0], [23])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114074,"parameters":{"A":[-23,0],"candidates":[-23,23,0,23],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-23,0],[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-20261011-r04-set-0075","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"候選元素的隸屬分割","stem_zh":"有限整數集合；A=[-24, 0]、候選原列=[-24, 24, 0, 24]。候選視作集合，依序列 (候選中屬A者, 候選中不屬A者)，各列遞增。","answer":{"kind":"expression","value":"([-24, 0], [24])","explanation_zh":"候選元素分割=([-24, 0], [24])。先去候選重複再判隸屬；A中未被列為候選的額外元素不進輸出。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["候選元素的隸屬分割"]},"variant":{"family_id":"qf-density11-set-candidate-partition","seed":202610114075,"parameters":{"A":[-24,0],"candidates":[-24,24,0,24],"operation":"density11_set_candidate_partition","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-candidate-partition/[[-24,0],[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-20261011-r04-set-0076","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[]]","explanation_zh":"有限冪集列舉=[[]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114076,"parameters":{"A":[],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[]"}},"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-20261011-r04-set-0077","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[0]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [0]]","explanation_zh":"有限冪集列舉=[[], [0]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114077,"parameters":{"A":[0],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[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-20261011-r04-set-0078","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-2, 1]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-2], [1], [-2, 1]]","explanation_zh":"有限冪集列舉=[[], [-2], [1], [-2, 1]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114078,"parameters":{"A":[-2,1],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-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-20261011-r04-set-0079","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-3, 0, 1, 3]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-3], [0], [1], [3], [-3, 0], [-3, 1], [-3, 3], [0, 1], [0, 3], [1, 3], [-3, 0, 1], [-3, 0, 3], [-3, 1, 3], [0, 1, 3], [-3, 0, 1, 3]]","explanation_zh":"有限冪集列舉=[[], [-3], [0], [1], [3], [-3, 0], [-3, 1], [-3, 3], [0, 1], [0, 3], [1, 3], [-3, 0, 1], [-3, 0, 3], [-3, 1, 3], [0, 1, 3], [-3, 0, 1, 3]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114079,"parameters":{"A":[-3,0,1,3],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-3,0,1,3]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r04-set-0080","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-4, 0, 1, 4]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-4], [0], [1], [4], [-4, 0], [-4, 1], [-4, 4], [0, 1], [0, 4], [1, 4], [-4, 0, 1], [-4, 0, 4], [-4, 1, 4], [0, 1, 4], [-4, 0, 1, 4]]","explanation_zh":"有限冪集列舉=[[], [-4], [0], [1], [4], [-4, 0], [-4, 1], [-4, 4], [0, 1], [0, 4], [1, 4], [-4, 0, 1], [-4, 0, 4], [-4, 1, 4], [0, 1, 4], [-4, 0, 1, 4]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114080,"parameters":{"A":[-4,0,1,4],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-4,0,1,4]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r04-set-0081","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-5, 0, 1, 5]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-5], [0], [1], [5], [-5, 0], [-5, 1], [-5, 5], [0, 1], [0, 5], [1, 5], [-5, 0, 1], [-5, 0, 5], [-5, 1, 5], [0, 1, 5], [-5, 0, 1, 5]]","explanation_zh":"有限冪集列舉=[[], [-5], [0], [1], [5], [-5, 0], [-5, 1], [-5, 5], [0, 1], [0, 5], [1, 5], [-5, 0, 1], [-5, 0, 5], [-5, 1, 5], [0, 1, 5], [-5, 0, 1, 5]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114081,"parameters":{"A":[-5,0,1,5],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-5,0,1,5]"}},"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-20261011-r04-set-0082","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-6, 0, 1, 6]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-6], [0], [1], [6], [-6, 0], [-6, 1], [-6, 6], [0, 1], [0, 6], [1, 6], [-6, 0, 1], [-6, 0, 6], [-6, 1, 6], [0, 1, 6], [-6, 0, 1, 6]]","explanation_zh":"有限冪集列舉=[[], [-6], [0], [1], [6], [-6, 0], [-6, 1], [-6, 6], [0, 1], [0, 6], [1, 6], [-6, 0, 1], [-6, 0, 6], [-6, 1, 6], [0, 1, 6], [-6, 0, 1, 6]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114082,"parameters":{"A":[-6,0,1,6],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-6,0,1,6]"}},"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-20261011-r04-set-0083","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-7, 0, 1, 7]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-7], [0], [1], [7], [-7, 0], [-7, 1], [-7, 7], [0, 1], [0, 7], [1, 7], [-7, 0, 1], [-7, 0, 7], [-7, 1, 7], [0, 1, 7], [-7, 0, 1, 7]]","explanation_zh":"有限冪集列舉=[[], [-7], [0], [1], [7], [-7, 0], [-7, 1], [-7, 7], [0, 1], [0, 7], [1, 7], [-7, 0, 1], [-7, 0, 7], [-7, 1, 7], [0, 1, 7], [-7, 0, 1, 7]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114083,"parameters":{"A":[-7,0,1,7],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-7,0,1,7]"}},"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-20261011-r04-set-0084","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-8, 0, 1, 8]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-8], [0], [1], [8], [-8, 0], [-8, 1], [-8, 8], [0, 1], [0, 8], [1, 8], [-8, 0, 1], [-8, 0, 8], [-8, 1, 8], [0, 1, 8], [-8, 0, 1, 8]]","explanation_zh":"有限冪集列舉=[[], [-8], [0], [1], [8], [-8, 0], [-8, 1], [-8, 8], [0, 1], [0, 8], [1, 8], [-8, 0, 1], [-8, 0, 8], [-8, 1, 8], [0, 1, 8], [-8, 0, 1, 8]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114084,"parameters":{"A":[-8,0,1,8],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-8,0,1,8]"}},"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-20261011-r04-set-0085","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-9, 0, 1, 9]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-9], [0], [1], [9], [-9, 0], [-9, 1], [-9, 9], [0, 1], [0, 9], [1, 9], [-9, 0, 1], [-9, 0, 9], [-9, 1, 9], [0, 1, 9], [-9, 0, 1, 9]]","explanation_zh":"有限冪集列舉=[[], [-9], [0], [1], [9], [-9, 0], [-9, 1], [-9, 9], [0, 1], [0, 9], [1, 9], [-9, 0, 1], [-9, 0, 9], [-9, 1, 9], [0, 1, 9], [-9, 0, 1, 9]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114085,"parameters":{"A":[-9,0,1,9],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-9,0,1,9]"}},"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-20261011-r04-set-0086","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-10, 0, 1, 10]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-10], [0], [1], [10], [-10, 0], [-10, 1], [-10, 10], [0, 1], [0, 10], [1, 10], [-10, 0, 1], [-10, 0, 10], [-10, 1, 10], [0, 1, 10], [-10, 0, 1, 10]]","explanation_zh":"有限冪集列舉=[[], [-10], [0], [1], [10], [-10, 0], [-10, 1], [-10, 10], [0, 1], [0, 10], [1, 10], [-10, 0, 1], [-10, 0, 10], [-10, 1, 10], [0, 1, 10], [-10, 0, 1, 10]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114086,"parameters":{"A":[-10,0,1,10],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-10,0,1,10]"}},"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-20261011-r04-set-0087","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-11, 0, 1, 11]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-11], [0], [1], [11], [-11, 0], [-11, 1], [-11, 11], [0, 1], [0, 11], [1, 11], [-11, 0, 1], [-11, 0, 11], [-11, 1, 11], [0, 1, 11], [-11, 0, 1, 11]]","explanation_zh":"有限冪集列舉=[[], [-11], [0], [1], [11], [-11, 0], [-11, 1], [-11, 11], [0, 1], [0, 11], [1, 11], [-11, 0, 1], [-11, 0, 11], [-11, 1, 11], [0, 1, 11], [-11, 0, 1, 11]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114087,"parameters":{"A":[-11,0,1,11],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-11,0,1,11]"}},"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-20261011-r04-set-0088","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-12, 0, 1, 12]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-12], [0], [1], [12], [-12, 0], [-12, 1], [-12, 12], [0, 1], [0, 12], [1, 12], [-12, 0, 1], [-12, 0, 12], [-12, 1, 12], [0, 1, 12], [-12, 0, 1, 12]]","explanation_zh":"有限冪集列舉=[[], [-12], [0], [1], [12], [-12, 0], [-12, 1], [-12, 12], [0, 1], [0, 12], [1, 12], [-12, 0, 1], [-12, 0, 12], [-12, 1, 12], [0, 1, 12], [-12, 0, 1, 12]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114088,"parameters":{"A":[-12,0,1,12],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-12,0,1,12]"}},"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-20261011-r04-set-0089","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-13, 0, 1, 13]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-13], [0], [1], [13], [-13, 0], [-13, 1], [-13, 13], [0, 1], [0, 13], [1, 13], [-13, 0, 1], [-13, 0, 13], [-13, 1, 13], [0, 1, 13], [-13, 0, 1, 13]]","explanation_zh":"有限冪集列舉=[[], [-13], [0], [1], [13], [-13, 0], [-13, 1], [-13, 13], [0, 1], [0, 13], [1, 13], [-13, 0, 1], [-13, 0, 13], [-13, 1, 13], [0, 1, 13], [-13, 0, 1, 13]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114089,"parameters":{"A":[-13,0,1,13],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-13,0,1,13]"}},"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-20261011-r04-set-0090","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-14, 0, 1, 14]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-14], [0], [1], [14], [-14, 0], [-14, 1], [-14, 14], [0, 1], [0, 14], [1, 14], [-14, 0, 1], [-14, 0, 14], [-14, 1, 14], [0, 1, 14], [-14, 0, 1, 14]]","explanation_zh":"有限冪集列舉=[[], [-14], [0], [1], [14], [-14, 0], [-14, 1], [-14, 14], [0, 1], [0, 14], [1, 14], [-14, 0, 1], [-14, 0, 14], [-14, 1, 14], [0, 1, 14], [-14, 0, 1, 14]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114090,"parameters":{"A":[-14,0,1,14],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-14,0,1,14]"}},"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-20261011-r04-set-0091","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-15, 0, 1, 15]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-15], [0], [1], [15], [-15, 0], [-15, 1], [-15, 15], [0, 1], [0, 15], [1, 15], [-15, 0, 1], [-15, 0, 15], [-15, 1, 15], [0, 1, 15], [-15, 0, 1, 15]]","explanation_zh":"有限冪集列舉=[[], [-15], [0], [1], [15], [-15, 0], [-15, 1], [-15, 15], [0, 1], [0, 15], [1, 15], [-15, 0, 1], [-15, 0, 15], [-15, 1, 15], [0, 1, 15], [-15, 0, 1, 15]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114091,"parameters":{"A":[-15,0,1,15],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-15,0,1,15]"}},"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-20261011-r04-set-0092","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-16, 0, 1, 16]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-16], [0], [1], [16], [-16, 0], [-16, 1], [-16, 16], [0, 1], [0, 16], [1, 16], [-16, 0, 1], [-16, 0, 16], [-16, 1, 16], [0, 1, 16], [-16, 0, 1, 16]]","explanation_zh":"有限冪集列舉=[[], [-16], [0], [1], [16], [-16, 0], [-16, 1], [-16, 16], [0, 1], [0, 16], [1, 16], [-16, 0, 1], [-16, 0, 16], [-16, 1, 16], [0, 1, 16], [-16, 0, 1, 16]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114092,"parameters":{"A":[-16,0,1,16],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-16,0,1,16]"}},"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-20261011-r04-set-0093","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-17, 0, 1, 17]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-17], [0], [1], [17], [-17, 0], [-17, 1], [-17, 17], [0, 1], [0, 17], [1, 17], [-17, 0, 1], [-17, 0, 17], [-17, 1, 17], [0, 1, 17], [-17, 0, 1, 17]]","explanation_zh":"有限冪集列舉=[[], [-17], [0], [1], [17], [-17, 0], [-17, 1], [-17, 17], [0, 1], [0, 17], [1, 17], [-17, 0, 1], [-17, 0, 17], [-17, 1, 17], [0, 1, 17], [-17, 0, 1, 17]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114093,"parameters":{"A":[-17,0,1,17],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-17,0,1,17]"}},"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-20261011-r04-set-0094","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-18, 0, 1, 18]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-18], [0], [1], [18], [-18, 0], [-18, 1], [-18, 18], [0, 1], [0, 18], [1, 18], [-18, 0, 1], [-18, 0, 18], [-18, 1, 18], [0, 1, 18], [-18, 0, 1, 18]]","explanation_zh":"有限冪集列舉=[[], [-18], [0], [1], [18], [-18, 0], [-18, 1], [-18, 18], [0, 1], [0, 18], [1, 18], [-18, 0, 1], [-18, 0, 18], [-18, 1, 18], [0, 1, 18], [-18, 0, 1, 18]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114094,"parameters":{"A":[-18,0,1,18],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-18,0,1,18]"}},"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-20261011-r04-set-0095","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-19, 0, 1, 19]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-19], [0], [1], [19], [-19, 0], [-19, 1], [-19, 19], [0, 1], [0, 19], [1, 19], [-19, 0, 1], [-19, 0, 19], [-19, 1, 19], [0, 1, 19], [-19, 0, 1, 19]]","explanation_zh":"有限冪集列舉=[[], [-19], [0], [1], [19], [-19, 0], [-19, 1], [-19, 19], [0, 1], [0, 19], [1, 19], [-19, 0, 1], [-19, 0, 19], [-19, 1, 19], [0, 1, 19], [-19, 0, 1, 19]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114095,"parameters":{"A":[-19,0,1,19],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-19,0,1,19]"}},"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-20261011-r04-set-0096","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-20, 0, 1, 20]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-20], [0], [1], [20], [-20, 0], [-20, 1], [-20, 20], [0, 1], [0, 20], [1, 20], [-20, 0, 1], [-20, 0, 20], [-20, 1, 20], [0, 1, 20], [-20, 0, 1, 20]]","explanation_zh":"有限冪集列舉=[[], [-20], [0], [1], [20], [-20, 0], [-20, 1], [-20, 20], [0, 1], [0, 20], [1, 20], [-20, 0, 1], [-20, 0, 20], [-20, 1, 20], [0, 1, 20], [-20, 0, 1, 20]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114096,"parameters":{"A":[-20,0,1,20],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-20,0,1,20]"}},"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-20261011-r04-set-0097","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-21, 0, 1, 21]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-21], [0], [1], [21], [-21, 0], [-21, 1], [-21, 21], [0, 1], [0, 21], [1, 21], [-21, 0, 1], [-21, 0, 21], [-21, 1, 21], [0, 1, 21], [-21, 0, 1, 21]]","explanation_zh":"有限冪集列舉=[[], [-21], [0], [1], [21], [-21, 0], [-21, 1], [-21, 21], [0, 1], [0, 21], [1, 21], [-21, 0, 1], [-21, 0, 21], [-21, 1, 21], [0, 1, 21], [-21, 0, 1, 21]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114097,"parameters":{"A":[-21,0,1,21],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-21,0,1,21]"}},"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-20261011-r04-set-0098","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-22, 0, 1, 22]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-22], [0], [1], [22], [-22, 0], [-22, 1], [-22, 22], [0, 1], [0, 22], [1, 22], [-22, 0, 1], [-22, 0, 22], [-22, 1, 22], [0, 1, 22], [-22, 0, 1, 22]]","explanation_zh":"有限冪集列舉=[[], [-22], [0], [1], [22], [-22, 0], [-22, 1], [-22, 22], [0, 1], [0, 22], [1, 22], [-22, 0, 1], [-22, 0, 22], [-22, 1, 22], [0, 1, 22], [-22, 0, 1, 22]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114098,"parameters":{"A":[-22,0,1,22],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-22,0,1,22]"}},"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-20261011-r04-set-0099","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-23, 0, 1, 23]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-23], [0], [1], [23], [-23, 0], [-23, 1], [-23, 23], [0, 1], [0, 23], [1, 23], [-23, 0, 1], [-23, 0, 23], [-23, 1, 23], [0, 1, 23], [-23, 0, 1, 23]]","explanation_zh":"有限冪集列舉=[[], [-23], [0], [1], [23], [-23, 0], [-23, 1], [-23, 23], [0, 1], [0, 23], [1, 23], [-23, 0, 1], [-23, 0, 23], [-23, 1, 23], [0, 1, 23], [-23, 0, 1, 23]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114099,"parameters":{"A":[-23,0,1,23],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-23,0,1,23]"}},"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-20261011-r04-set-0100","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","language":"zh-Hant","source_mko_ids":["mko-set"],"title_zh":"有限集合的完整冪集","stem_zh":"有限整數集合；A=[-24, 0, 1, 24]。列全部子集合；各子集遞增，外層先按大小再按數值字典序，空集合的冪集仍含空子集。","answer":{"kind":"expression","value":"[[], [-24], [0], [1], [24], [-24, 0], [-24, 1], [-24, 24], [0, 1], [0, 24], [1, 24], [-24, 0, 1], [-24, 0, 24], [-24, 1, 24], [0, 1, 24], [-24, 0, 1, 24]]","explanation_zh":"有限冪集列舉=[[], [-24], [0], [1], [24], [-24, 0], [-24, 1], [-24, 24], [0, 1], [0, 24], [1, 24], [-24, 0, 1], [-24, 0, 24], [-24, 1, 24], [0, 1, 24], [-24, 0, 1, 24]]。由空子集逐個元素分成取與不取兩支，再依指定次序列全；這是非無限制概括，沒有越過有限A。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限集合的完整冪集"]},"variant":{"family_id":"qf-density11-set-powerset-enumeration","seed":202610114100,"parameters":{"A":[-24,0,1,24],"operation":"density11_set_powerset_enumeration","domain":"finite_integer_set_slice","semantic_template":"qf-density11-set-powerset-enumeration/[-24,0,1,24]"}},"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"}}