{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260916-logic-conjunction-truth-0003",
  "pilot_number": "R0065-33028",
  "number": 33028,
  "family_id": "qf-logic-conjunction-truth",
  "title": {
    "zh-Hant": "第 33028 題：qf-logic-conjunction-truth",
    "en": "Question 33028: Truth of a Conjunction"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260916-logic-conjunction-truth-0003",
    "batch_id": "batch-20260916-logical-connectives",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-logical-connectives"
    ],
    "title_zh": "qf-logic-conjunction-truth",
    "stem_zh": "指定 P3 與 Q3 的真值分別為 真、假。P3 與 Q3 ∧ 的真值是否為真？",
    "answer": {
      "kind": "choice",
      "value": "否",
      "choices": [
        "是",
        "否"
      ],
      "explanation_zh": "P3 與 Q3：兩者都真，故本題值為 假。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 1,
      "skills": [
        "真值條件",
        "邏輯連接詞"
      ]
    },
    "variant": {
      "family_id": "qf-logic-conjunction-truth",
      "seed": 20260919,
      "parameters": {
        "P": true,
        "Q": false,
        "operator": "∧",
        "context": "P3 與 Q3",
        "semantic_template": "qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P3 與 Q3\",\"operator\":\"∧\"}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "schema_pending",
        "independent_recomputation_pending"
      ],
      "warning_zh": "本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "GPT-5.6 Terra",
      "generated_at": "2026-09-16",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260916-logic-conjunction-truth-0003",
    "batch_id": "batch-20260916-logical-connectives",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "bcfe5dc0cde63f9e3be5d59a33e64194e126400608955426f2440deb3daf2aa9",
      "family_id": "qf-logic-conjunction-truth",
      "seed": 20260919,
      "semantic_template": "qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P3 與 Q3\",\"operator\":\"∧\"}"
    },
    "fields": {
      "title": "Truth of a Conjunction",
      "stem": "The truth values of P and Q are true and false respectively. Is P ∧ Q true?",
      "answer": {
        "kind": "choice",
        "value": "No",
        "choices": [
          "Yes",
          "No"
        ],
        "explanation": "A conjunction is true exactly when both operands are true, so this value is false."
      },
      "skills": [
        "truth conditions",
        "logical connectives"
      ],
      "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": "指定 P3 與 Q3 的真值分別為 真、假。P3 與 Q3 ∧ 的真值是否為真？",
        "en": "The truth values of P and Q are true and false respectively. Is P ∧ Q true?"
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-logic-conjunction-truth, BASE-no-required-operation, BASE-no-required-domain, []]",
      "after": "derived = [[SOURCE_YesNo_STRING]]",
      "relation": "implies",
      "rule_id": "R65_SOURCE_bank_keys_operation_domain_ordered_output_roles",
      "conditions": [],
      "explanation": {
        "zh-Hant": "MOD25用LOCAL hyphen及具名domain，矩陣legacy用underscore/reals，BASElogic不補domain/op。輸出tuple/矩陣/數字欄與fraction文字各依來源，不一律保/1；原中英/AST/status不變。",
        "en": "MOD25 uses LOCAL hyphens/named domains,legacy matrices underscores/reals;BASE logic acquires no domain/op.Output tuples,matrices,numeric fields and fraction texts follow THIS source,not a universal/1 rule.Retain originals/English/AST/status."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以原始資料、型別、欄序、論域與明示前提反向核對；不表示結論唯一還原前提。有限來源候選、獨立審查、形式證明及發布各自分開。",
          "en": "Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [是, 否, ∧, \"P3 \\u8207 Q3\"]",
      "after": "derived = [[[否, 否, 否], [否, 是, 否], [是, 否, 否], [是, 是, 是]]]",
      "relation": "implies",
      "rule_id": "Logic_EXACT_Boolean_givens_FULL_connective_truth_definition",
      "conditions": [],
      "explanation": {
        "zh-Hant": "P/Q真值是給定的EXACT Boolean，不從context內容猜真偽。列四種完整定義；∨是含括或，→只在P真Q假為假，非因果；↔核兩方向。",
        "en": "P/Q are GIVEN EXACT Booleans;do not infer truth from context.Show all four defining cases.OR is INCLUSIVE;material implication fails ONLY at P true/Q false and is not causation;check BOTH directions for iff."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以原始資料、型別、欄序、論域與明示前提反向核對；不表示結論唯一還原前提。有限來源候選、獨立審查、形式證明及發布各自分開。",
          "en": "Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "source roles = [是, 否, ∧]",
      "after": "derived = [否, 是, 否, 是, 否]",
      "relation": "implies",
      "rule_id": "Logic_INSTANCE_forward_backward_and_result_not_underlying_proof",
      "conditions": [],
      "explanation": {
        "zh-Hant": "代入本題P/Q得到此連接詞真值；↔要兩方向同真。假前提的→可真，不等於證因果或證原命題已成立。",
        "en": "Substitute THIS P/Q to evaluate the connective;iff needs both directions true.A false-premise implication may be true without establishing causation or proving the underlying propositions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以原始資料、型別、欄序、論域與明示前提反向核對；不表示結論唯一還原前提。有限來源候選、獨立審查、形式證明及發布各自分開。",
          "en": "Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": "否"
  },
  "conclusion": {
    "canonical_value": "否",
    "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": {
    "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db",
    "question_binding": {
      "batch_id": "batch-20260916-logical-connectives",
      "batch_path": "public/data/questions/batches/batch-20260916-logical-connectives/questions.jsonl",
      "batch_sha256": "72d5ab1818fde69a41e4e3ddd7745e5947e9a97f6de2362b33f563260ce87a3f",
      "original_line": 3,
      "original_line_sha256": "f7a2d901f993f68a8e9522597e1b7e2fd3f4954a793cd1a2b865b118ce565e01",
      "question_compact_sha256": "bcfe5dc0cde63f9e3be5d59a33e64194e126400608955426f2440deb3daf2aa9",
      "english_row_compact_sha256": "c3c36c9be152cc9578ecd7fa535c51c33a618bcc76bb058fa823b5f1bf3e2db1",
      "english_manifest_path": "public/data/i18n/editions/batch-20260916-logical-connectives.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260916-logical-connectives.en.jsonl"
    },
    "mko_bindings": {
      "mko-logical-connectives": {
        "sha256": "d102be1d207477db8f00af868ed046578922ba9eeef220b0f6049bfca3964270",
        "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": "871e2c05026567a1deae741d6b90b0588100c6482ee167c7f9f45af5b72d8606",
    "original_candidate_sha256": "e28edd7d294c3fe95031a05b4fae0357059fe03b971a61aa83d7e5778347526c",
    "original_candidate_line_sha256": "e28edd7d294c3fe95031a05b4fae0357059fe03b971a61aa83d7e5778347526c"
  },
  "historical_source_state": {
    "review_state": {
      "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-20261026-012-p66",
    "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": "92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6",
      "question_first_witness_sha256": "012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 3,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "bca71e82a3b603522a7c8b63fcbc81f6ac763288e5b122c1663da40e54865d65",
      "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."
  }
}