{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0001","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(0)=∅，目標Fin(0)=∅，關係R的列項=[]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([0, 0], [], [], [], 0, [])","explanation_zh":"離散結構核對=([0, 0], [], [], [], 0, [])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173001,"parameters":{"n":0,"m":0,"pairs":[],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":0,\"n\":0,\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0002","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(0)=∅，關係R的列項=[]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([2, 0], [], [], [], 0, [0, 1])","explanation_zh":"離散結構核對=([2, 0], [], [], [], 0, [0, 1])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173002,"parameters":{"n":2,"m":0,"pairs":[],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":0,\"n\":2,\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0003","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(0)=∅，目標Fin(2)=[0, 1]，關係R的列項=[]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([0, 2], [], [], [], 0, [])","explanation_zh":"離散結構核對=([0, 2], [], [], [], 0, [])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173003,"parameters":{"n":0,"m":2,"pairs":[],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":2,\"n\":0,\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0004","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[[0, 0], [1, 1], [0, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([2, 2], [[0, 0], [1, 1]], [0, 1], [0, 1], 2, [])","explanation_zh":"離散結構核對=([2, 2], [[0, 0], [1, 1]], [0, 1], [0, 1], 2, [])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173004,"parameters":{"n":2,"m":2,"pairs":[[0,0],[1,1],[0,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":2,\"n\":2,\"pairs\":[[0,0],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0005","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[[0, 0], [0, 1]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([2, 2], [[0, 0], [0, 1]], [0], [0, 1], 2, [1])","explanation_zh":"離散結構核對=([2, 2], [[0, 0], [0, 1]], [0], [0, 1], 2, [1])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173005,"parameters":{"n":2,"m":2,"pairs":[[0,0],[0,1]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":2,\"n\":2,\"pairs\":[[0,0],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0006","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0]], [0], [0], 1, [1, 2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0]], [0], [0], 1, [1, 2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173006,"parameters":{"n":3,"m":3,"pairs":[[0,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0007","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1]], [0], [1], 1, [1, 2])","explanation_zh":"離散結構核對=([3, 3], [[0, 1]], [0], [1], 1, [1, 2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173007,"parameters":{"n":3,"m":3,"pairs":[[0,1]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0008","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1]], [0], [0, 1], 2, [1, 2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1]], [0], [0, 1], 2, [1, 2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173008,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0009","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2]], [0], [2], 1, [1, 2])","explanation_zh":"離散結構核對=([3, 3], [[0, 2]], [0], [2], 1, [1, 2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173009,"parameters":{"n":3,"m":3,"pairs":[[0,2]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0010","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 2]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 2]], [0], [0, 2], 2, [1, 2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 2]], [0], [0, 2], 2, [1, 2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173010,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,2]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0011","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [0, 2]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [0, 2]], [0], [1, 2], 2, [1, 2])","explanation_zh":"離散結構核對=([3, 3], [[0, 1], [0, 2]], [0], [1, 2], 2, [1, 2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173011,"parameters":{"n":3,"m":3,"pairs":[[0,1],[0,2]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0012","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [0, 2]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1], [0, 2]], [0], [0, 1, 2], 3, [1, 2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1], [0, 2]], [0], [0, 1, 2], 3, [1, 2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173012,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[0,2]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0013","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[1, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[1, 0]], [1], [0], 1, [0, 2])","explanation_zh":"離散結構核對=([3, 3], [[1, 0]], [1], [0], 1, [0, 2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173013,"parameters":{"n":3,"m":3,"pairs":[[1,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0014","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [1, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 0]], [0, 1], [0], 2, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [1, 0]], [0, 1], [0], 2, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173014,"parameters":{"n":3,"m":3,"pairs":[[0,0],[1,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0015","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [1, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 0]], [0, 1], [0, 1], 2, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 1], [1, 0]], [0, 1], [0, 1], 2, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173015,"parameters":{"n":3,"m":3,"pairs":[[0,1],[1,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0016","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [1, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1], [1, 0]], [0, 1], [0, 1], 3, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1], [1, 0]], [0, 1], [0, 1], 3, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173016,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[1,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0017","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2], [1, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 0]], [0, 1], [0, 2], 2, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 2], [1, 0]], [0, 1], [0, 2], 2, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173017,"parameters":{"n":3,"m":3,"pairs":[[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0018","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 2], [1, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 2], [1, 0]], [0, 1], [0, 2], 3, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 2], [1, 0]], [0, 1], [0, 2], 3, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173018,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0019","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [0, 2], [1, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [0, 2], [1, 0]], [0, 1], [0, 1, 2], 3, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 1], [0, 2], [1, 0]], [0, 1], [0, 1, 2], 3, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173019,"parameters":{"n":3,"m":3,"pairs":[[0,1],[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0020","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [0, 2], [1, 0]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1], [0, 2], [1, 0]], [0, 1], [0, 1, 2], 4, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1], [0, 2], [1, 0]], [0, 1], [0, 1, 2], 4, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173020,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0021","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[1, 1]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[1, 1]], [1], [1], 1, [0, 2])","explanation_zh":"離散結構核對=([3, 3], [[1, 1]], [1], [1], 1, [0, 2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173021,"parameters":{"n":3,"m":3,"pairs":[[1,1]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0022","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [1, 1]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 1]], [0, 1], [0, 1], 2, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [1, 1]], [0, 1], [0, 1], 2, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173022,"parameters":{"n":3,"m":3,"pairs":[[0,0],[1,1]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0023","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [1, 1]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 1]], [0, 1], [1], 2, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 1], [1, 1]], [0, 1], [1], 2, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173023,"parameters":{"n":3,"m":3,"pairs":[[0,1],[1,1]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0024","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [1, 1]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1], [1, 1]], [0, 1], [0, 1], 3, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1], [1, 1]], [0, 1], [0, 1], 3, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173024,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[1,1]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0025","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係兩個實際投影","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2], [1, 1]]。答 ([n,m], 正規有序對, 實際第一投影, 第二投影, 關係基數, 宣告來源中未出現的索引)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 1]], [0, 1], [1, 2], 2, [2])","explanation_zh":"離散結構核對=([3, 3], [[0, 2], [1, 1]], [0, 1], [1, 2], 2, [2])；先去重同一有序對，再各取第一、第二分量的集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係兩個實際投影"]},"variant":{"family_id":"qf-density17-relation-full-typed-inventory","seed":202610173025,"parameters":{"n":3,"m":3,"pairs":[[0,2],[1,1]],"domain":"Fin_typed_relation","operation":"relation-full-typed-inventory","semantic_template":"qf-density17-relation-full-typed-inventory/{\"m\":3,\"n\":3,\"pairs\":[[0,2],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0026","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(0)=∅，目標Fin(0)=∅，關係R的列項=[]。來源子集列項=[]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([], [], [], [])","explanation_zh":"離散結構核對=([], [], [], [])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173026,"parameters":{"n":0,"m":0,"pairs":[],"subset":[],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":0,\"n\":0,\"pairs\":[],\"subset\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0027","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[]。來源子集列項=[1]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([], [1], [], [[], []])","explanation_zh":"離散結構核對=([], [1], [], [[], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173027,"parameters":{"n":2,"m":2,"pairs":[],"subset":[1],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":2,\"n\":2,\"pairs\":[],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0028","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[[0, 0], [0, 1], [1, 1]]。來源子集列項=[]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [0, 1], [1, 1]], [], [], [[], []])","explanation_zh":"離散結構核對=([[0, 0], [0, 1], [1, 1]], [], [], [[], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173028,"parameters":{"n":2,"m":2,"pairs":[[0,0],[0,1],[1,1]],"subset":[],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":2,\"n\":2,\"pairs\":[[0,0],[0,1],[1,1]],\"subset\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0029","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[[0, 0], [0, 1], [1, 1]]。來源子集列項=[0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [0, 1], [1, 1]], [0], [0, 1], [[0], [0]])","explanation_zh":"離散結構核對=([[0, 0], [0, 1], [1, 1]], [0], [0, 1], [[0], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173029,"parameters":{"n":2,"m":2,"pairs":[[0,0],[0,1],[1,1]],"subset":[0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":2,\"n\":2,\"pairs\":[[0,0],[0,1],[1,1]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0030","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[[0, 0], [1, 1]]。來源子集列項=[1]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [1, 1]], [1], [1], [[], [1]])","explanation_zh":"離散結構核對=([[0, 0], [1, 1]], [1], [1], [[], [1]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173030,"parameters":{"n":2,"m":2,"pairs":[[0,0],[1,1]],"subset":[1],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":2,\"n\":2,\"pairs\":[[0,0],[1,1]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0031","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0]], [0, 2], [0], [[0], [], []])","explanation_zh":"離散結構核對=([[0, 0]], [0, 2], [0], [[0], [], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173031,"parameters":{"n":3,"m":3,"pairs":[[0,0]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0032","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 1]], [0, 2], [1], [[], [0], []])","explanation_zh":"離散結構核對=([[0, 1]], [0, 2], [1], [[], [0], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173032,"parameters":{"n":3,"m":3,"pairs":[[0,1]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,1]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0033","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [0, 1]], [0, 2], [0, 1], [[0], [0], []])","explanation_zh":"離散結構核對=([[0, 0], [0, 1]], [0, 2], [0, 1], [[0], [0], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173033,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0034","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 2]], [0, 2], [2], [[], [], [0]])","explanation_zh":"離散結構核對=([[0, 2]], [0, 2], [2], [[], [], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173034,"parameters":{"n":3,"m":3,"pairs":[[0,2]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,2]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0035","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 2]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [0, 2]], [0, 2], [0, 2], [[0], [], [0]])","explanation_zh":"離散結構核對=([[0, 0], [0, 2]], [0, 2], [0, 2], [[0], [], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173035,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,2]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,2]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0036","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [0, 2]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 1], [0, 2]], [0, 2], [1, 2], [[], [0], [0]])","explanation_zh":"離散結構核對=([[0, 1], [0, 2]], [0, 2], [1, 2], [[], [0], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173036,"parameters":{"n":3,"m":3,"pairs":[[0,1],[0,2]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[0,2]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0037","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [0, 2]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [0, 1], [0, 2]], [0, 2], [0, 1, 2], [[0], [0], [0]])","explanation_zh":"離散結構核對=([[0, 0], [0, 1], [0, 2]], [0, 2], [0, 1, 2], [[0], [0], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173037,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[0,2]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[0,2]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0038","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[1, 0]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[1, 0]], [0, 2], [], [[], [], []])","explanation_zh":"離散結構核對=([[1, 0]], [0, 2], [], [[], [], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173038,"parameters":{"n":3,"m":3,"pairs":[[1,0]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[1,0]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0039","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [1, 0]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [1, 0]], [0, 2], [0], [[0], [], []])","explanation_zh":"離散結構核對=([[0, 0], [1, 0]], [0, 2], [0], [[0], [], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173039,"parameters":{"n":3,"m":3,"pairs":[[0,0],[1,0]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[1,0]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0040","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [1, 0]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 1], [1, 0]], [0, 2], [1], [[], [0], []])","explanation_zh":"離散結構核對=([[0, 1], [1, 0]], [0, 2], [1], [[], [0], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173040,"parameters":{"n":3,"m":3,"pairs":[[0,1],[1,0]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[1,0]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0041","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [1, 0]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [0, 1], [1, 0]], [0, 2], [0, 1], [[0], [0], []])","explanation_zh":"離散結構核對=([[0, 0], [0, 1], [1, 0]], [0, 2], [0, 1], [[0], [0], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173041,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[1,0]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[1,0]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0042","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2], [1, 0]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 2], [1, 0]], [0, 2], [2], [[], [], [0]])","explanation_zh":"離散結構核對=([[0, 2], [1, 0]], [0, 2], [2], [[], [], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173042,"parameters":{"n":3,"m":3,"pairs":[[0,2],[1,0]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,2],[1,0]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0043","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 2], [1, 0]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [0, 2], [1, 0]], [0, 2], [0, 2], [[0], [], [0]])","explanation_zh":"離散結構核對=([[0, 0], [0, 2], [1, 0]], [0, 2], [0, 2], [[0], [], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173043,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,2],[1,0]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,2],[1,0]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0044","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [0, 2], [1, 0]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 1], [0, 2], [1, 0]], [0, 2], [1, 2], [[], [0], [0]])","explanation_zh":"離散結構核對=([[0, 1], [0, 2], [1, 0]], [0, 2], [1, 2], [[], [0], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173044,"parameters":{"n":3,"m":3,"pairs":[[0,1],[0,2],[1,0]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[0,2],[1,0]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0045","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [0, 2], [1, 0]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [0, 1], [0, 2], [1, 0]], [0, 2], [0, 1, 2], [[0], [0], [0]])","explanation_zh":"離散結構核對=([[0, 0], [0, 1], [0, 2], [1, 0]], [0, 2], [0, 1, 2], [[0], [0], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173045,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[0,2],[1,0]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[0,2],[1,0]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0046","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[1, 1]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[1, 1]], [0, 2], [], [[], [], []])","explanation_zh":"離散結構核對=([[1, 1]], [0, 2], [], [[], [], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173046,"parameters":{"n":3,"m":3,"pairs":[[1,1]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[1,1]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0047","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [1, 1]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [1, 1]], [0, 2], [0], [[0], [], []])","explanation_zh":"離散結構核對=([[0, 0], [1, 1]], [0, 2], [0], [[0], [], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173047,"parameters":{"n":3,"m":3,"pairs":[[0,0],[1,1]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[1,1]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0048","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [1, 1]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 1], [1, 1]], [0, 2], [1], [[], [0], []])","explanation_zh":"離散結構核對=([[0, 1], [1, 1]], [0, 2], [1], [[], [0], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173048,"parameters":{"n":3,"m":3,"pairs":[[0,1],[1,1]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[1,1]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0049","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [1, 1]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 0], [0, 1], [1, 1]], [0, 2], [0, 1], [[0], [0], []])","explanation_zh":"離散結構核對=([[0, 0], [0, 1], [1, 1]], [0, 2], [0, 1], [[0], [0], []])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173049,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[1,1]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[1,1]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0050","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"指定來源子集的關係像","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2], [1, 1]]。來源子集列項=[2, 0]。答 (全正規關係對, 正規子集, R[子集], 限制到子集後按所有目標列的纖維)。","answer":{"kind":"expression","value":"([[0, 2], [1, 1]], [0, 2], [2], [[], [], [0]])","explanation_zh":"離散結構核對=([[0, 2], [1, 1]], [0, 2], [2], [[], [], [0]])；全關係保留在首欄；像與纖維只篩第一分量落於子集的列。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定來源子集的關係像"]},"variant":{"family_id":"qf-density17-relation-subset-image-fibers","seed":202610173050,"parameters":{"n":3,"m":3,"pairs":[[0,2],[1,1]],"subset":[2,0],"domain":"Fin_typed_relation","operation":"relation-subset-image-fibers","semantic_template":"qf-density17-relation-subset-image-fibers/{\"m\":3,\"n\":3,\"pairs\":[[0,2],[1,1]],\"subset\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0051","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(0)=∅，目標Fin(0)=∅，關係R的列項=[]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([0, 0], [0, 0], [], [], [], 是)","explanation_zh":"離散結構核對=([0, 0], [0, 0], [], [], [], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173051,"parameters":{"n":0,"m":0,"pairs":[],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":0,\"n\":0,\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0052","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(0)=∅，關係R的列項=[]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([2, 0], [0, 2], [], [], [], 是)","explanation_zh":"離散結構核對=([2, 0], [0, 2], [], [], [], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173052,"parameters":{"n":2,"m":0,"pairs":[],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":0,\"n\":2,\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0053","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(0)=∅，目標Fin(2)=[0, 1]，關係R的列項=[]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([0, 2], [2, 0], [], [], [], 是)","explanation_zh":"離散結構核對=([0, 2], [2, 0], [], [], [], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173053,"parameters":{"n":0,"m":2,"pairs":[],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":2,\"n\":0,\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0054","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[[0, 0], [1, 1], [0, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([2, 2], [2, 2], [[0, 0], [1, 1]], [[0, 0], [1, 1]], [[0, 0], [1, 1]], 是)","explanation_zh":"離散結構核對=([2, 2], [2, 2], [[0, 0], [1, 1]], [[0, 0], [1, 1]], [[0, 0], [1, 1]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173054,"parameters":{"n":2,"m":2,"pairs":[[0,0],[1,1],[0,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":2,\"n\":2,\"pairs\":[[0,0],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0055","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[[0, 0], [0, 1]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([2, 2], [2, 2], [[0, 0], [0, 1]], [[0, 0], [1, 0]], [[0, 0], [0, 1]], 是)","explanation_zh":"離散結構核對=([2, 2], [2, 2], [[0, 0], [0, 1]], [[0, 0], [1, 0]], [[0, 0], [0, 1]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173055,"parameters":{"n":2,"m":2,"pairs":[[0,0],[0,1]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":2,\"n\":2,\"pairs\":[[0,0],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0056","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0]], [[0, 0]], [[0, 0]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0]], [[0, 0]], [[0, 0]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173056,"parameters":{"n":3,"m":3,"pairs":[[0,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0057","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 1]], [[1, 0]], [[0, 1]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 1]], [[1, 0]], [[0, 1]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173057,"parameters":{"n":3,"m":3,"pairs":[[0,1]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0058","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0], [0, 1]], [[0, 0], [1, 0]], [[0, 0], [0, 1]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0], [0, 1]], [[0, 0], [1, 0]], [[0, 0], [0, 1]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173058,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0059","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 2]], [[2, 0]], [[0, 2]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 2]], [[2, 0]], [[0, 2]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173059,"parameters":{"n":3,"m":3,"pairs":[[0,2]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0060","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 2]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0], [0, 2]], [[0, 0], [2, 0]], [[0, 0], [0, 2]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0], [0, 2]], [[0, 0], [2, 0]], [[0, 0], [0, 2]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173060,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,2]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0061","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [0, 2]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 1], [0, 2]], [[1, 0], [2, 0]], [[0, 1], [0, 2]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 1], [0, 2]], [[1, 0], [2, 0]], [[0, 1], [0, 2]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173061,"parameters":{"n":3,"m":3,"pairs":[[0,1],[0,2]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0062","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [0, 2]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0], [0, 1], [0, 2]], [[0, 0], [1, 0], [2, 0]], [[0, 0], [0, 1], [0, 2]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0], [0, 1], [0, 2]], [[0, 0], [1, 0], [2, 0]], [[0, 0], [0, 1], [0, 2]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173062,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[0,2]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0063","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[1, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[1, 0]], [[0, 1]], [[1, 0]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[1, 0]], [[0, 1]], [[1, 0]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173063,"parameters":{"n":3,"m":3,"pairs":[[1,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0064","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [1, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0], [1, 0]], [[0, 0], [0, 1]], [[0, 0], [1, 0]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0], [1, 0]], [[0, 0], [0, 1]], [[0, 0], [1, 0]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173064,"parameters":{"n":3,"m":3,"pairs":[[0,0],[1,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0065","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [1, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 1], [1, 0]], [[0, 1], [1, 0]], [[0, 1], [1, 0]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 1], [1, 0]], [[0, 1], [1, 0]], [[0, 1], [1, 0]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173065,"parameters":{"n":3,"m":3,"pairs":[[0,1],[1,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0066","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [1, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0], [0, 1], [1, 0]], [[0, 0], [0, 1], [1, 0]], [[0, 0], [0, 1], [1, 0]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0], [0, 1], [1, 0]], [[0, 0], [0, 1], [1, 0]], [[0, 0], [0, 1], [1, 0]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173066,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[1,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0067","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2], [1, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 2], [1, 0]], [[0, 1], [2, 0]], [[0, 2], [1, 0]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 2], [1, 0]], [[0, 1], [2, 0]], [[0, 2], [1, 0]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173067,"parameters":{"n":3,"m":3,"pairs":[[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0068","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 2], [1, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0], [0, 2], [1, 0]], [[0, 0], [0, 1], [2, 0]], [[0, 0], [0, 2], [1, 0]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0], [0, 2], [1, 0]], [[0, 0], [0, 1], [2, 0]], [[0, 0], [0, 2], [1, 0]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173068,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0069","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [0, 2], [1, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 1], [0, 2], [1, 0]], [[0, 1], [1, 0], [2, 0]], [[0, 1], [0, 2], [1, 0]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 1], [0, 2], [1, 0]], [[0, 1], [1, 0], [2, 0]], [[0, 1], [0, 2], [1, 0]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173069,"parameters":{"n":3,"m":3,"pairs":[[0,1],[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0070","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [0, 2], [1, 0]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0], [0, 1], [0, 2], [1, 0]], [[0, 0], [0, 1], [1, 0], [2, 0]], [[0, 0], [0, 1], [0, 2], [1, 0]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0], [0, 1], [0, 2], [1, 0]], [[0, 0], [0, 1], [1, 0], [2, 0]], [[0, 0], [0, 1], [0, 2], [1, 0]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173070,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0071","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[1, 1]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[1, 1]], [[1, 1]], [[1, 1]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[1, 1]], [[1, 1]], [[1, 1]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173071,"parameters":{"n":3,"m":3,"pairs":[[1,1]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0072","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [1, 1]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0], [1, 1]], [[0, 0], [1, 1]], [[0, 0], [1, 1]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0], [1, 1]], [[0, 0], [1, 1]], [[0, 0], [1, 1]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173072,"parameters":{"n":3,"m":3,"pairs":[[0,0],[1,1]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0073","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [1, 1]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 1], [1, 1]], [[1, 0], [1, 1]], [[0, 1], [1, 1]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 1], [1, 1]], [[1, 0], [1, 1]], [[0, 1], [1, 1]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173073,"parameters":{"n":3,"m":3,"pairs":[[0,1],[1,1]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0074","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [1, 1]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 0], [0, 1], [1, 1]], [[0, 0], [1, 0], [1, 1]], [[0, 0], [0, 1], [1, 1]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 0], [0, 1], [1, 1]], [[0, 0], [1, 0], [1, 1]], [[0, 0], [0, 1], [1, 1]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173074,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[1,1]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0075","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"有序關係交換兩次","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2], [1, 1]]。答 ([n,m], [m,n], 正規原關係對, 逆關係對, 再交換一次的對, 往返相等資格)。","answer":{"kind":"expression","value":"([3, 3], [3, 3], [[0, 2], [1, 1]], [[1, 1], [2, 0]], [[0, 2], [1, 1]], 是)","explanation_zh":"離散結構核對=([3, 3], [3, 3], [[0, 2], [1, 1]], [[1, 1], [2, 0]], [[0, 2], [1, 1]], 是)；每次交換有序對分量並交換型別，再按字典序列集合。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有序關係交換兩次"]},"variant":{"family_id":"qf-density17-relation-inverse-double","seed":202610173075,"parameters":{"n":3,"m":3,"pairs":[[0,2],[1,1]],"domain":"Fin_typed_relation","operation":"relation-inverse-double","semantic_template":"qf-density17-relation-inverse-double/{\"m\":3,\"n\":3,\"pairs\":[[0,2],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0076","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(0)=∅，目標Fin(0)=∅，關係R的列項=[]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([0, 0], [], [], 是, 是, [])","explanation_zh":"離散結構核對=([0, 0], [], [], 是, 是, [])；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173076,"parameters":{"n":0,"m":0,"pairs":[],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":0,\"n\":0,\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0077","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(0)=∅，關係R的列項=[]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([2, 0], [], [0, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([2, 0], [], [0, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173077,"parameters":{"n":2,"m":0,"pairs":[],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":0,\"n\":2,\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0078","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(0)=∅，目標Fin(2)=[0, 1]，關係R的列項=[]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([0, 2], [], [], 是, 是, [])","explanation_zh":"離散結構核對=([0, 2], [], [], 是, 是, [])；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173078,"parameters":{"n":0,"m":2,"pairs":[],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":2,\"n\":0,\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0079","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[[0, 0], [1, 1], [0, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([2, 2], [[0, 0], [1, 1]], [1, 1], 是, 是, [0, 1])","explanation_zh":"離散結構核對=([2, 2], [[0, 0], [1, 1]], [1, 1], 是, 是, [0, 1])；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173079,"parameters":{"n":2,"m":2,"pairs":[[0,0],[1,1],[0,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":2,\"n\":2,\"pairs\":[[0,0],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0080","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(2)=[0, 1]，目標Fin(2)=[0, 1]，關係R的列項=[[0, 0], [0, 1]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([2, 2], [[0, 0], [0, 1]], [2, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([2, 2], [[0, 0], [0, 1]], [2, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173080,"parameters":{"n":2,"m":2,"pairs":[[0,0],[0,1]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":2,\"n\":2,\"pairs\":[[0,0],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0081","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0]], [1, 0, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0]], [1, 0, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173081,"parameters":{"n":3,"m":3,"pairs":[[0,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0082","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 1]], [1, 0, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 1]], [1, 0, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173082,"parameters":{"n":3,"m":3,"pairs":[[0,1]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0083","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1]], [2, 0, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1]], [2, 0, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173083,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0084","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 2]], [1, 0, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 2]], [1, 0, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173084,"parameters":{"n":3,"m":3,"pairs":[[0,2]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0085","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 2]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 2]], [2, 0, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 2]], [2, 0, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173085,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,2]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0086","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [0, 2]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [0, 2]], [2, 0, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 1], [0, 2]], [2, 0, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173086,"parameters":{"n":3,"m":3,"pairs":[[0,1],[0,2]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0087","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [0, 2]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1], [0, 2]], [3, 0, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1], [0, 2]], [3, 0, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173087,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[0,2]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0088","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[1, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[1, 0]], [0, 1, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[1, 0]], [0, 1, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173088,"parameters":{"n":3,"m":3,"pairs":[[1,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0089","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [1, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 0]], [1, 1, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [1, 0]], [1, 1, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173089,"parameters":{"n":3,"m":3,"pairs":[[0,0],[1,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0090","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [1, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 0]], [1, 1, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 1], [1, 0]], [1, 1, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173090,"parameters":{"n":3,"m":3,"pairs":[[0,1],[1,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0091","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [1, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1], [1, 0]], [2, 1, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1], [1, 0]], [2, 1, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173091,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[1,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0092","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2], [1, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 0]], [1, 1, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 2], [1, 0]], [1, 1, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173092,"parameters":{"n":3,"m":3,"pairs":[[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0093","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 2], [1, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 2], [1, 0]], [2, 1, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 2], [1, 0]], [2, 1, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173093,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0094","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [0, 2], [1, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [0, 2], [1, 0]], [2, 1, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 1], [0, 2], [1, 0]], [2, 1, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173094,"parameters":{"n":3,"m":3,"pairs":[[0,1],[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0095","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [0, 2], [1, 0]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1], [0, 2], [1, 0]], [3, 1, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1], [0, 2], [1, 0]], [3, 1, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173095,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[0,2],[1,0]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[0,2],[1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0096","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[1, 1]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[1, 1]], [0, 1, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[1, 1]], [0, 1, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173096,"parameters":{"n":3,"m":3,"pairs":[[1,1]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0097","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [1, 1]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 1]], [1, 1, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [1, 1]], [1, 1, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173097,"parameters":{"n":3,"m":3,"pairs":[[0,0],[1,1]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0098","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 1], [1, 1]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 1]], [1, 1, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 1], [1, 1]], [1, 1, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173098,"parameters":{"n":3,"m":3,"pairs":[[0,1],[1,1]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0099","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 0], [0, 1], [1, 1]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [0, 1], [1, 1]], [2, 1, 0], 否, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 0], [0, 1], [1, 1]], [2, 1, 0], 否, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173099,"parameters":{"n":3,"m":3,"pairs":[[0,0],[0,1],[1,1]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,0],[0,1],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261017-r03-relation-0100","batch_id":"batch-20261012-advance-20261017-r03-relation-foundations","language":"zh-Hant","source_mko_ids":["mko-relation"],"title_zh":"關係是否恰為總函數","stem_zh":"明示Fin來源與目標，有序關係對。來源Fin(3)=[0, 1, 2]，目標Fin(3)=[0, 1, 2]，關係R的列項=[[0, 2], [1, 1]]。答 ([n,m], 正規關係對, 每個來源纖維大小, 單值資格, 每來源恰一值的總函數資格, 總表或不是總函數)。空來源的逐項條件按真處理。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 1]], [1, 1, 0], 是, 否, 不是總函數)","explanation_zh":"離散結構核對=([3, 3], [[0, 2], [1, 1]], [1, 1, 0], 是, 否, 不是總函數)；每個來源最多一值才單值，每個來源恰一值才可列總表。；有限精確核對不是一般形式證明；逆關係不自動是反函數；關係不必是總函數；重複列項按集合正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["關係是否恰為總函數"]},"variant":{"family_id":"qf-density17-relation-single-valued-total","seed":202610173100,"parameters":{"n":3,"m":3,"pairs":[[0,2],[1,1]],"domain":"Fin_typed_relation","operation":"relation-single-valued-total","semantic_template":"qf-density17-relation-single-valued-total/{\"m\":3,\"n\":3,\"pairs\":[[0,2],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}