{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0001","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"15ee47efdec9058e5d1ecb9e93d7d1f97bd148476c30ef9133c208ee04a8501e","family_id":"qf-logic-conjunction-truth","seed":20260917,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P1 與 Q1\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∧ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A conjunction is true exactly when both operands are true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0002","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3a8a1717efe0cad150044d43adcfcd8520b909a05f66f1f00d375508b76fa804","family_id":"qf-logic-conjunction-truth","seed":20260918,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P2 與 Q2\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false and true 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."}}
{"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0004","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc511bc524dac990634a3be37969a4745da6ce2016dc604cd2dcac2017b5e774","family_id":"qf-logic-conjunction-truth","seed":20260920,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P4 與 Q4\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0005","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54262fe992a72c6c5e3837697e0869af6f5c9c60ff9df0a905128b7775846efb","family_id":"qf-logic-conjunction-truth","seed":20260921,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P5 與 Q5\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∧ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A conjunction is true exactly when both operands are true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0006","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8f323d648bafd3dc8700fa8149fb9e4f69305050c92cbaba1e0b930606698fff","family_id":"qf-logic-conjunction-truth","seed":20260922,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P6 與 Q6\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false and true 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0007","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"304f6663d249fee2a920b1e2f5ff13b9bd0266f266eaf4c467c39299de3f7677","family_id":"qf-logic-conjunction-truth","seed":20260923,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P7 與 Q7\",\"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0008","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2e11085d274ed09f01d3804550044c4c66900712c33caede3f0bd951f7c6f1f0","family_id":"qf-logic-conjunction-truth","seed":20260924,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P8 與 Q8\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0009","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cd767b0b4140118d7e245639c9d5bfeacb73b7e76772e15fce7fd6bd80883edb","family_id":"qf-logic-conjunction-truth","seed":20260925,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P9 與 Q9\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∧ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A conjunction is true exactly when both operands are true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0010","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7020b67a045b8e0b779527f6e25299731ad6c5bff03c91730aa5b37535bdd78c","family_id":"qf-logic-conjunction-truth","seed":20260926,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P10 與 Q10\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false and true 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0011","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f14f3838d66adc2d9accf22d72a6f4c0d132b191e8d06d324a3aaae17a404b4","family_id":"qf-logic-conjunction-truth","seed":20260927,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P11 與 Q11\",\"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0012","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6cd0e85ba6f64f57c5d458b7b6729f03157be2da33a051f35dcd769e2150e9d1","family_id":"qf-logic-conjunction-truth","seed":20260928,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P12 與 Q12\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0013","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb66204e8167e4200197aa4c7ab57f2c287fe7766951432bace05852b69c785c","family_id":"qf-logic-conjunction-truth","seed":20260929,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P13 與 Q13\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∧ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A conjunction is true exactly when both operands are true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0014","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2699277b09861afe4c8c998b761ff5d0b5221eb873ed76bb71a02c2fe7a0c9c2","family_id":"qf-logic-conjunction-truth","seed":20260930,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P14 與 Q14\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false and true 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0015","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"451081bc2aae1c70aaabee440d45365677a4ffc787ca60bc37a450d4dd56b632","family_id":"qf-logic-conjunction-truth","seed":20260931,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P15 與 Q15\",\"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0016","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df556df58d90329f6b8e8ef6f1b53ad1a389306f3a8d7ff67ef5573a4a667f4a","family_id":"qf-logic-conjunction-truth","seed":20260932,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P16 與 Q16\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0017","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"70374796fef2bccdb22a51fe9938222d671e716a6a2e4b6c4809e89d812d6b8e","family_id":"qf-logic-conjunction-truth","seed":20260933,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P17 與 Q17\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∧ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A conjunction is true exactly when both operands are true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0018","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d19789d5b9b293ed70e97d02a8f0e178ed78756c8562817d7af01684325c2751","family_id":"qf-logic-conjunction-truth","seed":20260934,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P18 與 Q18\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false and true 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0019","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"899fd25c58cc1c2857524b4cf01f9308f931fac0514cef947affc568aeb30216","family_id":"qf-logic-conjunction-truth","seed":20260935,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P19 與 Q19\",\"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0020","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9628814c7ab2fc0c0a9e28b9091982715ee4398fe185e77a01846b13b3c113bd","family_id":"qf-logic-conjunction-truth","seed":20260936,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P20 與 Q20\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0021","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d80d66fc51cdd948dff4618726400950ac18028db7f8bdddd2bcea0a5d42d4b","family_id":"qf-logic-conjunction-truth","seed":20260937,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P21 與 Q21\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∧ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A conjunction is true exactly when both operands are true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0022","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c186fea569ebe1fff26146335869ae4684c0065bd50522dcb8216cd69e048efa","family_id":"qf-logic-conjunction-truth","seed":20260938,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P22 與 Q22\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false and true 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0023","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2ebcd6a08f11b01db6481dc6bac5d51fbe3c29dfe5cf889826db42e5e12dae01","family_id":"qf-logic-conjunction-truth","seed":20260939,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P23 與 Q23\",\"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0024","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3bbce31ae5c92f8a96622173d4b59e7e371f85419fe2dc147a2c617dff2c63e2","family_id":"qf-logic-conjunction-truth","seed":20260940,"semantic_template":"qf-logic-conjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P24 與 Q24\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are false 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-conjunction-truth-0025","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bdde8e8f09664ba0cb02655d2f1d164a662ba3aad24e7fb684462dffdca3fb63","family_id":"qf-logic-conjunction-truth","seed":20260941,"semantic_template":"qf-logic-conjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P25 與 Q25\",\"operator\":\"∧\"}"},"fields":{"title":"Truth of a Conjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∧ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A conjunction is true exactly when both operands are true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0001","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bfab0612f332e1892daf01c25ca0b7b60555ed95008bdab3f349829fc8618c67","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261017,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P1 與 Q1\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0002","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"447acc44c150db5b0f6787b869249b1c2e8fe3883c3e4cb9bf54651f18bd881e","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261018,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P2 與 Q2\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0003","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa168c38a41cfe2bf688f70cdfa6a5112571a57b809bb0d5286401e1c2905c31","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261019,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P3 與 Q3\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0004","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"72e6d2af9ed7d6fdbccde41cc98c8644b007bda00d2285627ed1e66c7ba3fa9b","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261020,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P4 與 Q4\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0005","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"853e7ed67eece19736a9540656050ff279fff0d92fded9cc2bb7e95839a2d264","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261021,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P5 與 Q5\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0006","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5034df26b4f24043b83a1f68a21f8b1dcbaa8d543621c978bd5a07b3100fc281","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261022,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P6 與 Q6\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0007","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"718047acdb94c56c7f46d31748f78d9acc24bddbabd391bb741f71bbfde2f008","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261023,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P7 與 Q7\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0008","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac25b162a91ed59d03ec956cf7951b0be2a7c1179a6ca2744b4f53c4c6541046","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261024,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P8 與 Q8\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0009","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae6a00060e8a87fe4c11db9ab85372d40850fdb4bc5f987a47b884e121d828b9","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261025,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P9 與 Q9\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0010","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87af60003540b9e79e2444dd074dbfee766197734936c869637d20e8baf5d4a1","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261026,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P10 與 Q10\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0011","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"95c0d71fdb99a76e2ddb31fb2b8cb4edb38fe8016420f49117ba82a0782ff7bf","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261027,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P11 與 Q11\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0012","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31d8b912bfec8f148b3513c741ba2cad5e95a249cbf3e010f3481214be456713","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261028,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P12 與 Q12\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0013","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bafaee235b8e3bd775c5a9f3c6e578963e29692490704cfede069fac4360f49f","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261029,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P13 與 Q13\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0014","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d6299b49d1b87345a927e72efb92397a2ecbd50a1d53d021eadc3ec668ec1e3","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261030,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P14 與 Q14\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0015","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1bd78d02b83cae9384d42b4ddc4c303f1fc9061580d9e3624acc9f351e2c571a","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261031,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P15 與 Q15\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0016","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7d2d30da04117fd5afdaebfdc0eba7ec79cf3e5c54de78a01e0831e0a4e80446","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261032,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P16 與 Q16\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0017","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"179ad3b1a416a398c88564ceda6aa7a1f5f6b161e145006c371773618c6f400a","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261033,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P17 與 Q17\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0018","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e02a2770b0bee1a1a8c6ddea2e8ba9d124cae8797594d2437cc6b336252df964","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261034,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P18 與 Q18\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0019","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"26aac880f55f899b5c7403a22180c37ba66e0a85d688602d20c853959e6fe9cc","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261035,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P19 與 Q19\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0020","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"810a70426077da94c2131a7079fca0355e2a71fed7c3086fdd93420078375a09","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261036,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P20 與 Q20\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0021","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"77c735d7529380ea69f9018499d50d0c47b6186acd3007869e421cce930663c1","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261037,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P21 與 Q21\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0022","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d84b4e4038689a1eeeb7f2cf91147e9a5e2524e3dfdffee579b72ebac882f02","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261038,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":true,\"context\":\"P22 與 Q22\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0023","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"783164bfbb0a70f52afad0de4a6a8ca97222e7620ff8559c7970f52922f4d0ac","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261039,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":false,\"context\":\"P23 與 Q23\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0024","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"769b54d632b079531c578656f76b97107b06377b680f30266c470f7fa657b519","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261040,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":false,\"Q\":false,\"context\":\"P24 與 Q24\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are false and false respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-inclusive-disjunction-truth-0025","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0a528cc7516bb91d810434d58e38b82c066405074e42df83754dce8cb73281b0","family_id":"qf-logic-inclusive-disjunction-truth","seed":20261041,"semantic_template":"qf-logic-inclusive-disjunction-truth/{\"P\":true,\"Q\":true,\"context\":\"P25 與 Q25\",\"operator\":\"∨\"}"},"fields":{"title":"Truth of an Inclusive Disjunction","stem":"The truth values of P and Q are true and true respectively. Is P ∨ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"An inclusive disjunction is true when at least one operand is true, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0001","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"140116bcdc3c96572ea53d5d8f552b2352ff31336576c62e52475fac1c34b571","family_id":"qf-logic-material-implication-truth","seed":20261117,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P1 與 Q1\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are true and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0002","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"636d15b71bd2bebd99f475f562ac9f70c29cec852c58eff63b6a40961d7f3dfa","family_id":"qf-logic-material-implication-truth","seed":20261118,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P2 與 Q2\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0003","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"352a8d65881f1aa355b4831f5d424a5a116f8d8a7313bfa8ccd6c1cbf04a7132","family_id":"qf-logic-material-implication-truth","seed":20261119,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P3 與 Q3\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","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":"Material implication is false only when P is true and Q is false; it is not a causal claim. 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0004","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81c49fcbd9074b4e5bd5fd72a77d74fbdd23264635ab7a192251ae02c73e99ef","family_id":"qf-logic-material-implication-truth","seed":20261120,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P4 與 Q4\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and false respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0005","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7dafe51cd042f70793bd04d06b9ec57b5b2909a3943ab4a7d4033094d010d349","family_id":"qf-logic-material-implication-truth","seed":20261121,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P5 與 Q5\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are true and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0006","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d97d444a691270d85c8a97dd6aecc188e527d1199c865502a55c2789fc205c4d","family_id":"qf-logic-material-implication-truth","seed":20261122,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P6 與 Q6\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0007","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e32313911620e839662c97435cbaf57dc5d739138d0717175062d2303cec2d8","family_id":"qf-logic-material-implication-truth","seed":20261123,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P7 與 Q7\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","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":"Material implication is false only when P is true and Q is false; it is not a causal claim. 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0008","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"674760659d9b537a1f0f0aefbf46807a4681e1d4f124f61958a938841459b7d3","family_id":"qf-logic-material-implication-truth","seed":20261124,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P8 與 Q8\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and false respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0009","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"46de5d002931b1085ba2f86ad066c780b38b29b10d393fd0edbe5fda0500fd38","family_id":"qf-logic-material-implication-truth","seed":20261125,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P9 與 Q9\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are true and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0010","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9857b41262a0f8297cb2a851df01c44c917774c651d5392c04132378afc8fe04","family_id":"qf-logic-material-implication-truth","seed":20261126,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P10 與 Q10\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0011","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"14fd4b00e114c3f0a4ac812af637cd388134071f22ba4abae3b6d767fe63b034","family_id":"qf-logic-material-implication-truth","seed":20261127,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P11 與 Q11\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","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":"Material implication is false only when P is true and Q is false; it is not a causal claim. 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0012","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b8a8b57dd5fb9431ab98e62e753960558de8a562c956711cc2f700e039334515","family_id":"qf-logic-material-implication-truth","seed":20261128,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P12 與 Q12\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and false respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0013","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c3eade01f1310c0c6c8c280d4e3b5529008ac22c8abf49c24fdf5e73ba4a173","family_id":"qf-logic-material-implication-truth","seed":20261129,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P13 與 Q13\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are true and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0014","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9af75524888c304cbc1574fcd82d08949ae335dad561006b29044b35360725c1","family_id":"qf-logic-material-implication-truth","seed":20261130,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P14 與 Q14\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0015","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a64b2653ddbfa0255d924dcb7af89764d0fb50719c82cb21904fe4c50a56611e","family_id":"qf-logic-material-implication-truth","seed":20261131,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P15 與 Q15\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","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":"Material implication is false only when P is true and Q is false; it is not a causal claim. 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0016","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"052c28b9a0485fa7d8d38e3d73aecbc2e7ce5005e32bea38ed896ebc45edf45c","family_id":"qf-logic-material-implication-truth","seed":20261132,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P16 與 Q16\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and false respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0017","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef35eba48eeaa40c11cd57c455cbe6f0f2ff175bd7527ad0b558b91cc4bdb0e8","family_id":"qf-logic-material-implication-truth","seed":20261133,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P17 與 Q17\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are true and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0018","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb69c49edd30f36cd6badd26bcd3c97635b883dcc0f820832535a822c5e3925f","family_id":"qf-logic-material-implication-truth","seed":20261134,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P18 與 Q18\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0019","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"175a7e0c88831527f253a6b74f689df662ad0946fb2b74c072b2e86255f976b6","family_id":"qf-logic-material-implication-truth","seed":20261135,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P19 與 Q19\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","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":"Material implication is false only when P is true and Q is false; it is not a causal claim. 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0020","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da54517495f5004f91fea040a59361b40a519abe77e31bb7c28d611f644398c7","family_id":"qf-logic-material-implication-truth","seed":20261136,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P20 與 Q20\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and false respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0021","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"990b282993ad8102bfe24d4fc27e081deec759988809264c1a86348603750712","family_id":"qf-logic-material-implication-truth","seed":20261137,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P21 與 Q21\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are true and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0022","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a028e7afffe3f4e125d743011685240361c7ed64d9adf25d8eed0cbf0d776da1","family_id":"qf-logic-material-implication-truth","seed":20261138,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":true,\"context\":\"P22 與 Q22\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0023","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"849cee6433445bf631f19443b7f128d0382ec45d0bb340d99f99a1131a714093","family_id":"qf-logic-material-implication-truth","seed":20261139,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":false,\"context\":\"P23 與 Q23\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","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":"Material implication is false only when P is true and Q is false; it is not a causal claim. 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0024","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ceafb9db1ccdbe1ae97dbf48481d6820fde9f250b5c8d5218dac1769fd9f9a7","family_id":"qf-logic-material-implication-truth","seed":20261140,"semantic_template":"qf-logic-material-implication-truth/{\"P\":false,\"Q\":false,\"context\":\"P24 與 Q24\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are false and false respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-material-implication-truth-0025","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"592c75160fb041736f8c9598143e5a315e86ddda239de5dcb7776edc5630b447","family_id":"qf-logic-material-implication-truth","seed":20261141,"semantic_template":"qf-logic-material-implication-truth/{\"P\":true,\"Q\":true,\"context\":\"P25 與 Q25\",\"operator\":\"→\"}"},"fields":{"title":"Truth of a Material Implication","stem":"The truth values of P and Q are true and true respectively. Is P → Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Material implication is false only when P is true and Q is false; it is not a causal claim. This value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0001","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a93efa1b8338ee973b99b6e6a48aa51a0a3f87909ff0d41f41975c6fd556206d","family_id":"qf-logic-biconditional-truth","seed":20261217,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P1 與 Q1\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are true and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0002","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e7b284ea36de3b4db5fc89fc450b10cb8000a1490beb3df341c93b5323e81c97","family_id":"qf-logic-biconditional-truth","seed":20261218,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P2 與 Q2\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0003","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1f3b15ef48aad846c9f4e8121bb56d9082e32e3414719e3d5a0b748fe42c1fa","family_id":"qf-logic-biconditional-truth","seed":20261219,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P3 與 Q3\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","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 biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0004","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f57c0b7f2fcfcdcff37a226079c354015cb275197e8e67715ffceaf46fe66402","family_id":"qf-logic-biconditional-truth","seed":20261220,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P4 與 Q4\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and false respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0005","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0cb8cde5703e84b30c0b746e491616abc24cd175a018527c4e6c3968362c8f54","family_id":"qf-logic-biconditional-truth","seed":20261221,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P5 與 Q5\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are true and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0006","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a981b7c53543bfb5f44bad66d4a596d88fc0a602ef5cfe2bcd1e03cb4bbefcbb","family_id":"qf-logic-biconditional-truth","seed":20261222,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P6 與 Q6\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0007","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d0c127efaf5fd525a8003055fd3babfb223871e0be11a7fa74e3e20215bc82d7","family_id":"qf-logic-biconditional-truth","seed":20261223,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P7 與 Q7\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","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 biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0008","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89c79c7da8493e677131d94e0713ac6c90d940ecd4b5b6206d65a9be15b45d4c","family_id":"qf-logic-biconditional-truth","seed":20261224,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P8 與 Q8\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and false respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0009","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eb2c8c56882fc6f4e939e656f9b9cb301ce4239bf39ed127c36dc2191de1543a","family_id":"qf-logic-biconditional-truth","seed":20261225,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P9 與 Q9\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are true and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0010","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"434a6894dbdefd26abbeb0497aa357b52bbc2052d2349dca4702f6d1e3cd3d15","family_id":"qf-logic-biconditional-truth","seed":20261226,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P10 與 Q10\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0011","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d9a81b2c2c98895b6dc3cb8a128b985580b090b41d9c9112294638d9d9924c84","family_id":"qf-logic-biconditional-truth","seed":20261227,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P11 與 Q11\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","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 biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0012","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bbbc3475654c3c8cdca3f3916404d8f2eba19d43358b846129c405a279232df3","family_id":"qf-logic-biconditional-truth","seed":20261228,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P12 與 Q12\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and false respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0013","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b75679eb68b53062f2bf2bcfdc41b24af63a8f7b1e3df7b654ccb40079c35bf9","family_id":"qf-logic-biconditional-truth","seed":20261229,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P13 與 Q13\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are true and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0014","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04463ef9b28859558bbf2a8a6516af2c315a9fcc88d0d2bfafca430e1335a71a","family_id":"qf-logic-biconditional-truth","seed":20261230,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P14 與 Q14\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0015","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64aaf7e93f6a18bd90a2b9ab00cb21fd0f36e7787ad334632b928d9d1755643c","family_id":"qf-logic-biconditional-truth","seed":20261231,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P15 與 Q15\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","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 biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0016","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"226e8925db895caf6f268ba70f75cfadd94b6601db7c5a40f610a40bd93eb08b","family_id":"qf-logic-biconditional-truth","seed":20261232,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P16 與 Q16\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and false respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0017","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"60ef4d5dc2f72925cf03f5acaea0ff27a30588855b1954e66483e466e66df42f","family_id":"qf-logic-biconditional-truth","seed":20261233,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P17 與 Q17\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are true and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0018","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c90d41e857b8c7310c0c8f3f16a40b932a116c69a5b3e6c7a30bc58041fdb87e","family_id":"qf-logic-biconditional-truth","seed":20261234,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P18 與 Q18\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0019","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68d8ebfd4248c00a1f9e6d0d39d82d88280b7de860c301eab4a07c8edfb3eaec","family_id":"qf-logic-biconditional-truth","seed":20261235,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P19 與 Q19\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","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 biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0020","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e178dddd594b53f24df87e33ef4bac377ada6238aee5ffe1da26e31c1fb4a2e","family_id":"qf-logic-biconditional-truth","seed":20261236,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P20 與 Q20\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and false respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0021","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec5826635b7f4b9763b1c651099a70ef62679fcd9b87656dba2bab65245190bf","family_id":"qf-logic-biconditional-truth","seed":20261237,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P21 與 Q21\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are true and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0022","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4d616462211af2266af7fdad72dfe38e4ea8b0e57bb63ff45b0bc45630a4a70","family_id":"qf-logic-biconditional-truth","seed":20261238,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":true,\"context\":\"P22 與 Q22\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0023","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3bfa1610d71968ec8b93b1dae13646c75e263b3c465923034b0ff6aa3ff087a5","family_id":"qf-logic-biconditional-truth","seed":20261239,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":false,\"context\":\"P23 與 Q23\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","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 biconditional is true exactly when both directions have the same truth value, 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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0024","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8ac90b8c421ed01e38474f0600a1d992080cfadd6ad7a3194b65fd68fffb6e2","family_id":"qf-logic-biconditional-truth","seed":20261240,"semantic_template":"qf-logic-biconditional-truth/{\"P\":false,\"Q\":false,\"context\":\"P24 與 Q24\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are false and false respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260916-logic-biconditional-truth-0025","batch_id":"batch-20260916-logical-connectives","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e207fe3509cfd3c5ee12a468c43d90e105cdd4f8474d5ccf738a0ff3577a9f88","family_id":"qf-logic-biconditional-truth","seed":20261241,"semantic_template":"qf-logic-biconditional-truth/{\"P\":true,\"Q\":true,\"context\":\"P25 與 Q25\",\"operator\":\"↔\"}"},"fields":{"title":"Truth of a Biconditional","stem":"The truth values of P and Q are true and true respectively. Is P ↔ Q true?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"A biconditional is true exactly when both directions have the same truth value, so this value is true."},"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."}}