{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0001","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135001,"parameters":{"A":[0,0,0,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0002","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 1, 1, 1, 1, 1, 1, 1]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [真, 真, 真, 真, 真, 真, 真, 真])","explanation_zh":"合取與含括析取表=([真, 真, 真, 真, 真, 真, 真, 真], [真, 真, 真, 真, 真, 真, 真, 真])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135002,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,1,1,1,1,1,1,1],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0003","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 0, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 假, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135003,"parameters":{"A":[1,0,0,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0004","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 0, 0, 0, 0, 0, 0]、B=[1, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([真, 假, 假, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([真, 假, 假, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135004,"parameters":{"A":[1,0,0,0,0,0,0,0],"B":[1,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0005","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 0, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 假, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135005,"parameters":{"A":[0,1,0,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0006","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135006,"parameters":{"A":[1,1,0,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0007","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 0]、B=[1, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([真, 假, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([真, 假, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135007,"parameters":{"A":[1,1,0,0,0,0,0,0],"B":[1,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[1,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0008","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 0, 0, 0, 0, 0, 0]、B=[0, 1, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 真, 假, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 真, 假, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135008,"parameters":{"A":[0,1,0,0,0,0,0,0],"B":[0,1,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0009","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 0]、B=[0, 1, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 真, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 真, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135009,"parameters":{"A":[1,1,0,0,0,0,0,0],"B":[0,1,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,1,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0010","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 0]、B=[1, 1, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([真, 真, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([真, 真, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135010,"parameters":{"A":[1,1,0,0,0,0,0,0],"B":[1,1,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[1,1,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0011","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 1, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135011,"parameters":{"A":[0,0,1,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0012","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 假, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135012,"parameters":{"A":[1,0,1,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0013","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 0]、B=[1, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([真, 假, 假, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([真, 假, 假, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135013,"parameters":{"A":[1,0,1,0,0,0,0,0],"B":[1,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[1,0,0,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0014","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 1, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 假, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135014,"parameters":{"A":[0,1,1,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0015","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 假, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135015,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0016","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[1, 0, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([真, 假, 假, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([真, 假, 假, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135016,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[1,0,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[1,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0017","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 1, 0, 0, 0, 0, 0]、B=[0, 1, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 真, 假, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 真, 假, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135017,"parameters":{"A":[0,1,1,0,0,0,0,0],"B":[0,1,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,1,0,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0018","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[0, 1, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 真, 假, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 真, 假, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135018,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[0,1,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0019","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[1, 1, 0, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([真, 真, 假, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([真, 真, 假, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135019,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[1,1,0,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[1,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0020","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 1, 0, 0, 0, 0, 0]、B=[0, 0, 1, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135020,"parameters":{"A":[0,0,1,0,0,0,0,0],"B":[0,0,1,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0021","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 0]、B=[0, 0, 1, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 真, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 真, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135021,"parameters":{"A":[1,0,1,0,0,0,0,0],"B":[0,0,1,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0022","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 0]、B=[1, 0, 1, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([真, 假, 真, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([真, 假, 真, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135022,"parameters":{"A":[1,0,1,0,0,0,0,0],"B":[1,0,1,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[1,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0023","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 1, 0, 0, 0, 0, 0]、B=[0, 0, 1, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 真, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 真, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135023,"parameters":{"A":[0,1,1,0,0,0,0,0],"B":[0,0,1,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,1,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0024","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[0, 0, 1, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([假, 假, 真, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([假, 假, 真, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135024,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[0,0,1,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[0,0,1,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0025","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列合取與含括析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[1, 0, 1, 0, 0, 0, 0, 0]。依序列 (A∧B真假表, A∨B含括析取真假表)。","answer":{"kind":"expression","value":"([真, 假, 真, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"合取與含括析取表=([真, 假, 真, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])。各列兩真才合取真，至少一真即含括析取真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列合取與含括析取"]},"variant":{"family_id":"qf-density13-connectives-and-or-table","seed":202610135025,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[1,0,1,0,0,0,0,0],"operation":"density13_connectives_and_or_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-and-or-table/[[1,0,1,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0026","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [真, 真, 真, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 真, 真, 真, 真, 真, 真], [真, 真, 真, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135026,"parameters":{"A":[0,0,0,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0027","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"材料蘊涵與雙條件表=([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135027,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0028","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 1]、B=[1, 0, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [假, 真, 真, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 真, 真, 真, 真, 真, 真], [假, 真, 真, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135028,"parameters":{"A":[0,0,0,0,0,0,0,1],"B":[1,0,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0029","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 0, 0, 0, 0, 0, 1]、B=[0, 0, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([假, 真, 真, 真, 真, 真, 真, 真], [假, 真, 真, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([假, 真, 真, 真, 真, 真, 真, 真], [假, 真, 真, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135029,"parameters":{"A":[1,0,0,0,0,0,0,1],"B":[0,0,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0030","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 1]、B=[0, 1, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [真, 假, 真, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 真, 真, 真, 真, 真, 真], [真, 假, 真, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135030,"parameters":{"A":[0,0,0,0,0,0,0,1],"B":[0,1,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[1,0,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0031","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 1]、B=[1, 1, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135031,"parameters":{"A":[0,0,0,0,0,0,0,1],"B":[1,1,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[0,0,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0032","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 0, 0, 0, 0, 0, 1]、B=[0, 1, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([假, 真, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([假, 真, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135032,"parameters":{"A":[1,0,0,0,0,0,0,1],"B":[0,1,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,1,1,1,1,1,1],[0,0,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0033","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 0, 0, 0, 0, 0, 1]、B=[0, 0, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 假, 真, 真, 真, 真, 真, 真], [真, 假, 真, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 假, 真, 真, 真, 真, 真, 真], [真, 假, 真, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135033,"parameters":{"A":[0,1,0,0,0,0,0,1],"B":[0,0,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,0,1,1,1,1,1,1],[1,0,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0034","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 0, 0, 0, 0, 0, 1]、B=[1, 0, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 假, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 假, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135034,"parameters":{"A":[0,1,0,0,0,0,0,1],"B":[1,0,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,0,1,1,1,1,1,1],[0,0,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0035","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 1]、B=[0, 0, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([假, 假, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([假, 假, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135035,"parameters":{"A":[1,1,0,0,0,0,0,1],"B":[0,0,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[0,0,1,1,1,1,1,1],[0,0,1,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0036","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 1]、B=[0, 0, 1, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [真, 真, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 真, 真, 真, 真, 真, 真], [真, 真, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135036,"parameters":{"A":[0,0,0,0,0,0,0,1],"B":[0,0,1,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[1,1,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0037","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 1]、B=[1, 0, 1, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 真, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135037,"parameters":{"A":[0,0,0,0,0,0,0,1],"B":[1,0,1,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[0,1,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0038","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 0, 0, 0, 0, 0, 1]、B=[0, 0, 1, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([假, 真, 真, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([假, 真, 真, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135038,"parameters":{"A":[1,0,0,0,0,0,0,1],"B":[0,0,1,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,1,1,1,1,1,1],[0,1,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0039","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 1]、B=[0, 1, 1, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [真, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 真, 真, 真, 真, 真, 真], [真, 假, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135039,"parameters":{"A":[0,0,0,0,0,0,0,1],"B":[0,1,1,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[1,0,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0040","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 1]、B=[1, 1, 1, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 真, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135040,"parameters":{"A":[0,0,0,0,0,0,0,1],"B":[1,1,1,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,1,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0041","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 0, 0, 0, 0, 0, 1]、B=[0, 1, 1, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([假, 真, 真, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([假, 真, 真, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135041,"parameters":{"A":[1,0,0,0,0,0,0,1],"B":[0,1,1,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,1,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0042","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 0, 0, 0, 0, 0, 1]、B=[0, 0, 1, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 假, 真, 真, 真, 真, 真, 真], [真, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 假, 真, 真, 真, 真, 真, 真], [真, 假, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135042,"parameters":{"A":[0,1,0,0,0,0,0,1],"B":[0,0,1,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,0,1,1,1,1,1,1],[1,0,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0043","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 0, 0, 0, 0, 0, 1]、B=[1, 0, 1, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 假, 真, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 假, 真, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135043,"parameters":{"A":[0,1,0,0,0,0,0,1],"B":[1,0,1,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,0,1,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0044","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 1]、B=[0, 0, 1, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([假, 假, 真, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([假, 假, 真, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135044,"parameters":{"A":[1,1,0,0,0,0,0,1],"B":[0,0,1,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[0,0,1,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0045","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 1, 0, 0, 0, 0, 1]、B=[0, 0, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 假, 真, 真, 真, 真, 真], [真, 真, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 假, 真, 真, 真, 真, 真], [真, 真, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135045,"parameters":{"A":[0,0,1,0,0,0,0,1],"B":[0,0,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,0,1,1,1,1,1],[1,1,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0046","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 1, 0, 0, 0, 0, 1]、B=[1, 0, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 假, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 假, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135046,"parameters":{"A":[0,0,1,0,0,0,0,1],"B":[1,0,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,0,1,1,1,1,1],[0,1,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0047","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 1]、B=[0, 0, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([假, 真, 假, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([假, 真, 假, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135047,"parameters":{"A":[1,0,1,0,0,0,0,1],"B":[0,0,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,0,1,1,1,1,1],[0,1,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0048","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 1, 0, 0, 0, 0, 1]、B=[0, 1, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 假, 真, 真, 真, 真, 真], [真, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 假, 真, 真, 真, 真, 真], [真, 假, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135048,"parameters":{"A":[0,0,1,0,0,0,0,1],"B":[0,1,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,0,1,1,1,1,1],[1,0,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0049","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 1, 0, 0, 0, 0, 1]、B=[1, 1, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([真, 真, 假, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([真, 真, 假, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135049,"parameters":{"A":[0,0,1,0,0,0,0,1],"B":[1,1,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[1,1,0,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0050","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列材料蘊涵與雙條件","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 1]、B=[0, 1, 0, 0, 0, 0, 0, 1]。依序列 (A→B材料蘊涵真假表, A↔B雙條件真假表)。","answer":{"kind":"expression","value":"([假, 真, 假, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"材料蘊涵與雙條件表=([假, 真, 假, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])。材料蘊涵只在前真後假時假，雙條件要求兩欄同真值；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列材料蘊涵與雙條件"]},"variant":{"family_id":"qf-density13-connectives-implication-biconditional","seed":202610135050,"parameters":{"A":[1,0,1,0,0,0,0,1],"B":[0,1,0,0,0,0,0,1],"operation":"density13_connectives_implication_biconditional","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-implication-biconditional/[[0,1,0,1,1,1,1,1],[0,0,0,1,1,1,1,1]]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0051","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [真, 真, 真, 真, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 真, 真, 真, 真, 真, 真, 真], [真, 真, 真, 真, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135051,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,1,1,1,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0052","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 1, 1, 1, 1, 1, 1, 1]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"兩路德摩根表=([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135052,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,1,1,1,1,1,1,1],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,0,0,0,0,0,0,0]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0053","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 0, 0, 0, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 真, 真, 真, 真, 真, 真, 真], [假, 真, 真, 真, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 真, 真, 真, 真, 真, 真, 真], [假, 真, 真, 真, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135053,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,0,0,0,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,1,1,1,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0054","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 1, 0, 0, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 假, 真, 真, 真, 真, 真, 真], [真, 假, 真, 真, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 假, 真, 真, 真, 真, 真, 真], [真, 假, 真, 真, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135054,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,1,0,0,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,0,1,1,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0055","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 1, 0, 0, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 假, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 假, 真, 真, 真, 真, 真, 真], [假, 假, 真, 真, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135055,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,1,0,0,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,0,1,1,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0056","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 0, 1, 0, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 真, 假, 真, 真, 真, 真, 真], [真, 真, 假, 真, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 真, 假, 真, 真, 真, 真, 真], [真, 真, 假, 真, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135056,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,0,1,0,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,1,0,1,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0057","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 0, 1, 0, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 真, 假, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 真, 假, 真, 真, 真, 真, 真], [假, 真, 假, 真, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135057,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,0,1,0,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,1,0,1,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0058","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 1, 1, 0, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 假, 假, 真, 真, 真, 真, 真], [真, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 假, 假, 真, 真, 真, 真, 真], [真, 假, 假, 真, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135058,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,1,1,0,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,0,0,1,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0059","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 1, 1, 0, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 假, 假, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 假, 假, 真, 真, 真, 真, 真], [假, 假, 假, 真, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135059,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,1,1,0,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,0,0,1,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0060","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 0, 0, 1, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 真, 真, 假, 真, 真, 真, 真], [真, 真, 真, 假, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 真, 真, 假, 真, 真, 真, 真], [真, 真, 真, 假, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135060,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,0,0,1,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,1,1,0,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0061","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 0, 0, 1, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 真, 真, 假, 真, 真, 真, 真], [假, 真, 真, 假, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 真, 真, 假, 真, 真, 真, 真], [假, 真, 真, 假, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135061,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,0,0,1,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,1,1,0,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0062","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 1, 0, 1, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 假, 真, 假, 真, 真, 真, 真], [真, 假, 真, 假, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 假, 真, 假, 真, 真, 真, 真], [真, 假, 真, 假, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135062,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,1,0,1,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,0,1,0,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0063","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 1, 0, 1, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 假, 真, 假, 真, 真, 真, 真], [假, 假, 真, 假, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 假, 真, 假, 真, 真, 真, 真], [假, 假, 真, 假, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135063,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,1,0,1,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,0,1,0,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0064","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 0, 1, 1, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 真, 假, 假, 真, 真, 真, 真], [真, 真, 假, 假, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 真, 假, 假, 真, 真, 真, 真], [真, 真, 假, 假, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135064,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,0,1,1,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,1,0,0,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0065","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 0, 1, 1, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 真, 假, 假, 真, 真, 真, 真], [假, 真, 假, 假, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 真, 假, 假, 真, 真, 真, 真], [假, 真, 假, 假, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135065,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,0,1,1,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,1,0,0,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0066","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 1, 1, 1, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 假, 假, 假, 真, 真, 真, 真], [真, 假, 假, 假, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 假, 假, 假, 真, 真, 真, 真], [真, 假, 假, 假, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135066,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,1,1,1,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,0,0,0,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0067","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 1, 1, 1, 0, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 真, 真, 真, 真], [假, 假, 假, 假, 真, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 假, 假, 假, 真, 真, 真, 真], [假, 假, 假, 假, 真, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135067,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,1,1,1,0,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,0,0,0,1,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0068","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 0, 0, 0, 1, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 假, 真, 真, 真], [真, 真, 真, 真, 假, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 真, 真, 真, 假, 真, 真, 真], [真, 真, 真, 真, 假, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135068,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,0,0,0,1,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,1,1,1,0,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0069","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 0, 0, 0, 1, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 真, 真, 真, 假, 真, 真, 真], [假, 真, 真, 真, 假, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 真, 真, 真, 假, 真, 真, 真], [假, 真, 真, 真, 假, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135069,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,0,0,0,1,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,1,1,1,0,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0070","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 1, 0, 0, 1, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 假, 真, 真, 假, 真, 真, 真], [真, 假, 真, 真, 假, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 假, 真, 真, 假, 真, 真, 真], [真, 假, 真, 真, 假, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135070,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,1,0,0,1,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,0,1,1,0,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0071","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 1, 0, 0, 1, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 假, 真, 真, 假, 真, 真, 真], [假, 假, 真, 真, 假, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 假, 真, 真, 假, 真, 真, 真], [假, 假, 真, 真, 假, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135071,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,1,0,0,1,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,0,1,1,0,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0072","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 0, 1, 0, 1, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 真, 假, 真, 假, 真, 真, 真], [真, 真, 假, 真, 假, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 真, 假, 真, 假, 真, 真, 真], [真, 真, 假, 真, 假, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135072,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,0,1,0,1,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,1,0,1,0,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0073","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 0, 1, 0, 1, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 真, 假, 真, 假, 真, 真, 真], [假, 真, 假, 真, 假, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 真, 假, 真, 假, 真, 真, 真], [假, 真, 假, 真, 假, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135073,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,0,1,0,1,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,1,0,1,0,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0074","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[0, 1, 1, 0, 1, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([真, 假, 假, 真, 假, 真, 真, 真], [真, 假, 假, 真, 假, 真, 真, 真])","explanation_zh":"兩路德摩根表=([真, 假, 假, 真, 假, 真, 真, 真], [真, 假, 假, 真, 假, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135074,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[0,1,1,0,1,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[1,0,0,1,0,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0075","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列的兩路德摩根值","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 1, 1, 0, 1, 0, 0, 0]。依序列 (¬(A∧B)真假表, ¬A∨¬B真假表)，兩條路各完整列出。","answer":{"kind":"expression","value":"([假, 假, 假, 真, 假, 真, 真, 真], [假, 假, 假, 真, 假, 真, 真, 真])","explanation_zh":"兩路德摩根表=([假, 假, 假, 真, 假, 真, 真, 真], [假, 假, 假, 真, 假, 真, 真, 真])。第一路先合取再否定，第二路分別否定再含括析取；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列的兩路德摩根值"]},"variant":{"family_id":"qf-density13-connectives-demorgan-table","seed":202610135075,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,1,1,0,1,0,0,0],"operation":"density13_connectives_demorgan_table","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-demorgan-table/[0,0,0,1,0,1,1,1]"}},"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":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0076","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 0, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([假, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135076,"parameters":{"A":[0,0,0,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0077","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 1, 1, 1, 1, 1]、B=[1, 1, 1, 1, 1, 1, 1, 1]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 真, 真, 真, 真, 真, 真], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 真, 真, 真, 真, 真, 真], [假, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135077,"parameters":{"A":[1,1,1,1,1,1,1,1],"B":[1,1,1,1,1,1,1,1],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,1,1,1,1,1],[0,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0078","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 0, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 假, 假, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 假, 假, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135078,"parameters":{"A":[1,0,0,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0079","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 0, 0, 0, 0, 0, 0]、B=[1, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 假, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135079,"parameters":{"A":[1,0,0,0,0,0,0,0],"B":[1,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0080","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 0, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([假, 真, 假, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([假, 真, 假, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135080,"parameters":{"A":[0,1,0,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0081","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 假, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135081,"parameters":{"A":[1,1,0,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,0,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0082","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 0]、B=[1, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 假, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 假, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135082,"parameters":{"A":[1,1,0,0,0,0,0,0],"B":[1,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0083","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 0, 0, 0, 0, 0, 0]、B=[0, 1, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([假, 真, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([假, 真, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135083,"parameters":{"A":[0,1,0,0,0,0,0,0],"B":[0,1,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0084","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 0]、B=[0, 1, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 假, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 假, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135084,"parameters":{"A":[1,1,0,0,0,0,0,0],"B":[0,1,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0085","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 0, 0, 0, 0, 0, 0]、B=[1, 1, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 假, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135085,"parameters":{"A":[1,1,0,0,0,0,0,0],"B":[1,1,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0086","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 1, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([假, 假, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([假, 假, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135086,"parameters":{"A":[0,0,1,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0087","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 假, 真, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 假, 真, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135087,"parameters":{"A":[1,0,1,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0088","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 0]、B=[1, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 假, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 假, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135088,"parameters":{"A":[1,0,1,0,0,0,0,0],"B":[1,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0089","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 1, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([假, 真, 真, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([假, 真, 真, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135089,"parameters":{"A":[0,1,1,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,1,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0090","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[0, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 真, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 真, 假, 假, 假, 假, 假], [真, 真, 真, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135090,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[0,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[1,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0091","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[1, 0, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 真, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 真, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135091,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[1,0,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0092","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 1, 0, 0, 0, 0, 0]、B=[0, 1, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([假, 真, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([假, 真, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135092,"parameters":{"A":[0,1,1,0,0,0,0,0],"B":[0,1,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0093","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[0, 1, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 真, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 真, 假, 假, 假, 假, 假], [真, 假, 真, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135093,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[0,1,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[1,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0094","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[1, 1, 0, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 真, 假, 假, 假, 假, 假], [假, 假, 真, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135094,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[1,1,0,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0095","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 0, 1, 0, 0, 0, 0, 0]、B=[0, 0, 1, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([假, 假, 真, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([假, 假, 真, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135095,"parameters":{"A":[0,0,1,0,0,0,0,0],"B":[0,0,1,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0096","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 0]、B=[0, 0, 1, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 假, 真, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 假, 真, 假, 假, 假, 假, 假], [真, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135096,"parameters":{"A":[1,0,1,0,0,0,0,0],"B":[0,0,1,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0097","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 0, 1, 0, 0, 0, 0, 0]、B=[1, 0, 1, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 假, 真, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 假, 真, 假, 假, 假, 假, 假], [假, 假, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135097,"parameters":{"A":[1,0,1,0,0,0,0,0],"B":[1,0,1,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0098","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[0, 1, 1, 0, 0, 0, 0, 0]、B=[0, 0, 1, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([假, 真, 真, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([假, 真, 真, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135098,"parameters":{"A":[0,1,1,0,0,0,0,0],"B":[0,0,1,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[0,1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0099","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[0, 0, 1, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 真, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 真, 假, 假, 假, 假, 假], [真, 真, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135099,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[0,0,1,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[1,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261009-advance-20261013-r05-logical-connectives-0100","batch_id":"batch-20261009-advance-20261013-r05-logical-connectives-foundations","language":"zh-Hant","source_mko_ids":["mko-logical-connectives"],"title_zh":"八列含括與排他析取","stem_zh":"古典八列完整真假表；列索引0到7，1為真、0為假，A=[1, 1, 1, 0, 0, 0, 0, 0]、B=[1, 0, 1, 0, 0, 0, 0, 0]。依序列 (含括A∨B真假表, 恰一真XOR真假表)，不要混同兩者。","answer":{"kind":"expression","value":"([真, 真, 真, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])","explanation_zh":"含括與排他析取表=([真, 真, 真, 假, 假, 假, 假, 假], [假, 真, 假, 假, 假, 假, 假, 假])。含括允許兩真，排他只允許恰一真；材料蘊涵非因果，有限表非全部推理規則證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["八列含括與排他析取"]},"variant":{"family_id":"qf-density13-connectives-inclusion-vs-xor","seed":202610135100,"parameters":{"A":[1,1,1,0,0,0,0,0],"B":[1,0,1,0,0,0,0,0],"operation":"density13_connectives_inclusion_vs_xor","domain":"finite_classical_eight_row_tables","semantic_template":"qf-density13-connectives-inclusion-vs-xor/[[1,1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-09","contract_version":"ocme-question-factory-v0.1"}}