{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261009-advance-20261013-r05-logical-connectives-0023",
  "pilot_number": "R0010-05923",
  "number": 5923,
  "family_id": "qf-density13-connectives-and-or-table",
  "title": {
    "zh-Hant": "第 5923 題：八列合取與含括析取",
    "en": "Question 5923: Conjunction and Inclusive Disjunction Tables"
  },
  "original_question": {
    "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"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261009-advance-20261013-r05-logical-connectives-0023",
    "batch_id": "batch-20261009-advance-20261013-r05-logical-connectives-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "dd774556592e20dddfaa642e55a1082e3e417b39a8106bd821aacebd88355dc2",
      "family_id": "qf-density13-connectives-and-or-table",
      "seed": 202610135023,
      "semantic_template": "qf-density13-connectives-and-or-table/[[0,0,1,0,0,0,0,0],[0,1,1,0,0,0,0,0]]"
    },
    "fields": {
      "title": "Conjunction and Inclusive Disjunction Tables",
      "stem": "Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).",
      "answer": {
        "kind": "expression",
        "value": "([False, False, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])",
        "explanation": "Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])."
      },
      "skills": [
        "Conjunction and Inclusive Disjunction Tables"
      ],
      "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."
    }
  },
  "givens": [
    {
      "id": "G001",
      "text": {
        "zh-Hant": "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)。",
        "en": "Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "given8 rows A=[0, 1, 1, 0, 0, 0, 0, 0];B=[0, 0, 1, 0, 0, 0, 0, 0]",
      "after": "classical Boolean values;read all supplied rows in order0,...,7",
      "relation": "implies",
      "rule_id": "classical_eight_row_connective_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "1為真、0為假；完整讀這八列，不假裝任意給定八列必已涵蓋所有賦值或已證全部推理規則。材料蘊涵也不是因果。",
        "en": "Interpret1 as True and0 as False and read all eight supplied rows.Do not assume arbitrary eight rows exhaust all valuations or prove every inference rule.Material implication is not causation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "row=0;A=假;B=假",
      "after": "A∧B=假;A∨B=假",
      "relation": "implies",
      "rule_id": "and_inclusive_or_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "合取要兩個都真，含括析取只要至少一真，允許兩真。",
        "en": "Conjunction requires both true;inclusive disjunction requires at least one true and permits both."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "row=1;A=真;B=假",
      "after": "A∧B=假;A∨B=真",
      "relation": "implies",
      "rule_id": "and_inclusive_or_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "合取要兩個都真，含括析取只要至少一真，允許兩真。",
        "en": "Conjunction requires both true;inclusive disjunction requires at least one true and permits both."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "row=2;A=真;B=真",
      "after": "A∧B=真;A∨B=真",
      "relation": "implies",
      "rule_id": "and_inclusive_or_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "合取要兩個都真，含括析取只要至少一真，允許兩真。",
        "en": "Conjunction requires both true;inclusive disjunction requires at least one true and permits both."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "row=3;A=假;B=假",
      "after": "A∧B=假;A∨B=假",
      "relation": "implies",
      "rule_id": "and_inclusive_or_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "合取要兩個都真，含括析取只要至少一真，允許兩真。",
        "en": "Conjunction requires both true;inclusive disjunction requires at least one true and permits both."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "row=4;A=假;B=假",
      "after": "A∧B=假;A∨B=假",
      "relation": "implies",
      "rule_id": "and_inclusive_or_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "合取要兩個都真，含括析取只要至少一真，允許兩真。",
        "en": "Conjunction requires both true;inclusive disjunction requires at least one true and permits both."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "row=5;A=假;B=假",
      "after": "A∧B=假;A∨B=假",
      "relation": "implies",
      "rule_id": "and_inclusive_or_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "合取要兩個都真，含括析取只要至少一真，允許兩真。",
        "en": "Conjunction requires both true;inclusive disjunction requires at least one true and permits both."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "row=6;A=假;B=假",
      "after": "A∧B=假;A∨B=假",
      "relation": "implies",
      "rule_id": "and_inclusive_or_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "合取要兩個都真，含括析取只要至少一真，允許兩真。",
        "en": "Conjunction requires both true;inclusive disjunction requires at least one true and permits both."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "row=7;A=假;B=假",
      "after": "A∧B=假;A∨B=假",
      "relation": "implies",
      "rule_id": "and_inclusive_or_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "合取要兩個都真，含括析取只要至少一真，允許兩真。",
        "en": "Conjunction requires both true;inclusive disjunction requires at least one true and permits both."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "([假, 假, 真, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])",
      "after": "complete ordered results of the two requested connectives",
      "relation": "implies",
      "rule_id": "complete_given_connective_rows",
      "conditions": [],
      "explanation": {
        "zh-Hant": "兩欄各保留原八列次序；這是給定古典表的逐列核對，不把數值一致或真假表標記當一般形式證明。",
        "en": "Each output column retains all eight original rows.This checks the given classical table rowwise,not a general formal proof inferred from matching values or table labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      [
        false,
        false,
        true,
        false,
        false,
        false,
        false,
        false
      ],
      [
        false,
        true,
        true,
        false,
        false,
        false,
        false,
        false
      ]
    ]
  },
  "conclusion": {
    "canonical_value": "([假, 假, 真, 假, 假, 假, 假, 假], [假, 真, 真, 假, 假, 假, 假, 假])",
    "explanation": {
      "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。",
      "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged."
    }
  },
  "definition_note": {
    "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。",
    "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate."
  },
  "source": {
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    "question_binding": {
      "batch_id": "batch-20261009-advance-20261013-r05-logical-connectives-foundations",
      "batch_path": "public/data/questions/batches/batch-20261009-advance-20261013-r05-logical-connectives-foundations/questions.jsonl",
      "batch_sha256": "baf48848d69d6b91e4e9a66849ac1717a3302fd9d228aae176bc9d98378861a6",
      "original_line": 23,
      "original_line_sha256": "afb5b0e16881c483aa9df1c223bec7dbd28f9365daaaa982f398d314027e0fa1",
      "question_compact_sha256": "dd774556592e20dddfaa642e55a1082e3e417b39a8106bd821aacebd88355dc2",
      "english_row_compact_sha256": "0de5ec6400fa824a295663909ac21237513c854b78b66c87fd37e579a31f8332",
      "english_manifest_path": "public/data/i18n/editions/batch-20261009-advance-20261013-r05-logical-connectives-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261009-advance-20261013-r05-logical-connectives-foundations.en.jsonl"
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    "mko_bindings": {
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        "english_sha256": "e154036107025c087a386a9c0cd8abed85ff1311e7f1e0ba3d6eea5c6357b87a",
        "original_path": "public/data/mko/logical-connectives.json",
        "english_path": "public/data/i18n/editions/mko-logical-connectives.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "aeab777a3897ae2c01315b86b5e9b9a43ffb59b075efae44fd95d447123d32f1",
    "original_candidate_sha256": "94bf878d401e170281df39dc487ca5c5afccb76f84cd37c1cc996cb94d40a6f5",
    "original_candidate_line_sha256": "94bf878d401e170281df39dc487ca5c5afccb76f84cd37c1cc996cb94d40a6f5"
  },
  "historical_source_state": {
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      "derivation": "candidate_authored_and_locally_checked",
      "source_question_state": "candidate",
      "independent_AI_or_human_review": "NOT_PERFORMED",
      "formalization": "not_formalized",
      "Lean": "NOT_RUN"
    },
    "scope_note": {
      "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。",
      "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged."
    },
    "label": "Frozen producer metadata; current per-question review is separate below."
  },
  "revision": {
    "id": "review-20261026-005-p11",
    "review_date": "2026-10-26",
    "owner_authorized_reader_publication": true,
    "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.",
    "review_receipts": {
      "semantic_review_sha256": "0328166a2e335aac7a5fb34556e68c80ba7d16612e822b3999c8ac348a9ca06f",
      "question_first_witness_sha256": "0da18e4e6cf71ece5ec5f00dd0cd161217b6d251672bc0b46d79fe7e6253f5fc"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 10,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "b690ed33626a9faecdc71e49be6de3bdf94b97bc860f22aa7701d2d2da789229",
      "arithmetic_steps": 0
    },
    "uses_answer_as_premise": false,
    "human_review": "NOT_PERFORMED",
    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
  }
}