{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260913-natural-number-membership-0001","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f35b7c1cbca49790a79b4f6a3c69ebdc3154248878f2a2f237975175f0bd655f","family_id":"qf-natural-number-membership","seed":20260913,"semantic_template":"natural/zero/value-0"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 0 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"0 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0002","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"abb37908cc060805815ee689609a4d3340421d7956cfb57e9fbcbb674b87fc0c","family_id":"qf-natural-number-membership","seed":20260914,"semantic_template":"natural/positive_integer/value-1"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 1 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"1 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0003","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc4b6c4dd664599ab527e44f7e1ffffdecdf8632b86ab9e9f207a794e311212c","family_id":"qf-natural-number-membership","seed":20260915,"semantic_template":"natural/positive_integer/value-2"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 2 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"2 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0004","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2218644d0e64e49ad64d1d81b461d9dfa765f8aed655ff341fd17417f6533484","family_id":"qf-natural-number-membership","seed":20260916,"semantic_template":"natural/positive_integer/value-5"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 5 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"5 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0005","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e44aed3b91aa75abbf94a5e8af605eb22e5fb51663afe288567b704ab80f52c3","family_id":"qf-natural-number-membership","seed":20260917,"semantic_template":"natural/positive_integer/value-10"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 10 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"10 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0006","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"66f45953b15e7690e5a1ae83590bf5b647b08b81d7deaafebe461e05d147ba02","family_id":"qf-natural-number-membership","seed":20260918,"semantic_template":"natural/positive_integer/value-25"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 25 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"25 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0007","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00f3d1f37e15033152c5a74ceb09f83d57c2536062d6eb8310b3df3186eb6085","family_id":"qf-natural-number-membership","seed":20260919,"semantic_template":"natural/positive_integer/value-100"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 100 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"100 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0008","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"644e571fd605450214af7538ca784e64fd28c8807ba47683b98ccaf3aaceecfe","family_id":"qf-natural-number-membership","seed":20260920,"semantic_template":"natural/positive_integer/value-7"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 7 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"7 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0009","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"675ac9be7c60babb26a02df566159e9cb8b0ae4b82fb6974cfc1d18b023ce16f","family_id":"qf-natural-number-membership","seed":20260921,"semantic_template":"natural/positive_integer/value-3"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 3 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"3 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0010","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d6e86c7d5e6db994586224e58f89aac23dbefa39ce07ca62d4fbdf66a0969201","family_id":"qf-natural-number-membership","seed":20260922,"semantic_template":"natural/positive_integer/value-12"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 12 belong to N?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"12 is a nonnegative integer, so it belongs to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0011","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b24a412c7a06b612ff81b9ec6e45fa5eafa8263d92cdd1e661479a49b5607e7","family_id":"qf-natural-number-membership","seed":20260923,"semantic_template":"natural/negative_integer/value--1"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does -1 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-1 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0012","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"de794f9251cdc5740acadf7a154943f4d70d31a33833510287038c2c1934ab69","family_id":"qf-natural-number-membership","seed":20260924,"semantic_template":"natural/negative_integer/value--2"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does -2 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-2 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0013","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a7d6e593c5641a4a9795a75d04b63590621fb5ba3df0cadbfcf2d3dae410208e","family_id":"qf-natural-number-membership","seed":20260925,"semantic_template":"natural/negative_integer/value--10"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does -10 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-10 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0014","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a1aa33b1ce3b36b37192a352886ce0dcc17b001d2b68e70b0e156c23814b9002","family_id":"qf-natural-number-membership","seed":20260926,"semantic_template":"natural/negative_integer/value--25"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does -25 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-25 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0015","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"88b48e9a383d8fb94b9417a8cf00528d67e9e2e228467921c5b50178e5eb5b8b","family_id":"qf-natural-number-membership","seed":20260927,"semantic_template":"natural/negative_integer/value--100"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does -100 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-100 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0016","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0444d81e779d947baef87f63a7a4768a79a2227d2ad109366c73bc76c752171","family_id":"qf-natural-number-membership","seed":20260928,"semantic_template":"natural/non_integer/value--0.5"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does -0.5 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-0.5 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0017","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a702cba71f877b89bf18faef1dbe386eb79f2c1526bf7ea84fb7a05f837907c","family_id":"qf-natural-number-membership","seed":20260929,"semantic_template":"natural/non_integer/value-0.5"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 0.5 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"0.5 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0018","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f3662e3469b38fb7677ec23d7d19eb2f263eed1f78c97df2dc741a32514dca9c","family_id":"qf-natural-number-membership","seed":20260930,"semantic_template":"natural/non_integer/value-1.5"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 1.5 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"1.5 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0019","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e5c46d4d5f8d8dcf8cd3dd89da3327e86c6192d7721169322bfa66335b43d821","family_id":"qf-natural-number-membership","seed":20260931,"semantic_template":"natural/non_integer/value-2.25"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does 2.25 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"2.25 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-natural-number-membership-0020","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"84f0e6c9327f9d2dce133012738e69f7cb24aa8b81cd8a0a2d7b97e6d22908fe","family_id":"qf-natural-number-membership","seed":20260932,"semantic_template":"natural/non_integer/value--3.75"},"fields":{"title":"Natural-Number Membership","stem":"Under this OCME entry's convention that N includes 0, does -3.75 belong to N?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-3.75 is not a nonnegative integer, so it does not belong to N under this entry's convention."},"skills":["natural-number convention","set membership"],"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-20260913-finite-set-membership-0001","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b951fcc0597e8d5aa58aeb8593961cdf8f8f7563e4e94a3be7a0a495bf95fb4","family_id":"qf-finite-set-membership","seed":20260933,"semantic_template":"finite-set/listed_element/elements-1,2/query-2"},"fields":{"title":"Finite Set Membership","stem":"Let A={1, 2} be an explicitly enumerated finite set. Does 2 satisfy 2∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"2 occurs in the explicit enumeration of A, so 2∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0002","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ddea9ca8edf6bc6b75bf3349eaa6796d03573ecb52dfe3d86ba27112ac755af","family_id":"qf-finite-set-membership","seed":20260934,"semantic_template":"finite-set/unlisted_element/elements-11,12,13/query-18"},"fields":{"title":"Finite Set Membership","stem":"Let A={11, 12, 13} be an explicitly enumerated finite set. Does 18 satisfy 18∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"18 does not occur in the explicit enumeration of A, so 18∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0003","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fab1b50b42c0126c8e21cc2a1bfd29d16e3a5e78f6508a872aa11faba1065855","family_id":"qf-finite-set-membership","seed":20260935,"semantic_template":"finite-set/listed_element/elements-21,22,23,24/query-24"},"fields":{"title":"Finite Set Membership","stem":"Let A={21, 22, 23, 24} be an explicitly enumerated finite set. Does 24 satisfy 24∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"24 occurs in the explicit enumeration of A, so 24∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0004","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"428572d784d461abd0fbb04d3981aa8efbb3550144a643741cc7f8c9f304521e","family_id":"qf-finite-set-membership","seed":20260936,"semantic_template":"finite-set/unlisted_element/elements-31,32/query-37"},"fields":{"title":"Finite Set Membership","stem":"Let A={31, 32} be an explicitly enumerated finite set. Does 37 satisfy 37∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"37 does not occur in the explicit enumeration of A, so 37∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0005","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53db8a01bdb8a2b8aa4fda1a27eb8137acffcc3de19c7de1b4770a5005d72533","family_id":"qf-finite-set-membership","seed":20260937,"semantic_template":"finite-set/listed_element/elements-41,42,43/query-43"},"fields":{"title":"Finite Set Membership","stem":"Let A={41, 42, 43} be an explicitly enumerated finite set. Does 43 satisfy 43∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"43 occurs in the explicit enumeration of A, so 43∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0006","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ddceaeb794935a2e57999745a54da1793f40acabc2e53d6a94c97045c05da6d4","family_id":"qf-finite-set-membership","seed":20260938,"semantic_template":"finite-set/unlisted_element/elements-51,52,53,54/query-59"},"fields":{"title":"Finite Set Membership","stem":"Let A={51, 52, 53, 54} be an explicitly enumerated finite set. Does 59 satisfy 59∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"59 does not occur in the explicit enumeration of A, so 59∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0007","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d393a215f10f03c0b2aab8f4666df893604347745b23a7fcd42ccffcc7faa66c","family_id":"qf-finite-set-membership","seed":20260939,"semantic_template":"finite-set/listed_element/elements-61,62/query-62"},"fields":{"title":"Finite Set Membership","stem":"Let A={61, 62} be an explicitly enumerated finite set. Does 62 satisfy 62∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"62 occurs in the explicit enumeration of A, so 62∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0008","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cce7f134fcac4a57552ceb58552f8f27654c465da3a170f96d21590fe210f3f8","family_id":"qf-finite-set-membership","seed":20260940,"semantic_template":"finite-set/unlisted_element/elements-71,72,73/query-78"},"fields":{"title":"Finite Set Membership","stem":"Let A={71, 72, 73} be an explicitly enumerated finite set. Does 78 satisfy 78∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"78 does not occur in the explicit enumeration of A, so 78∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0009","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a796e6a7524f758de3e9e4597bcca7c5dde024f5b4b6109d4cee32c19edab3e","family_id":"qf-finite-set-membership","seed":20260941,"semantic_template":"finite-set/listed_element/elements-81,82,83,84/query-82"},"fields":{"title":"Finite Set Membership","stem":"Let A={81, 82, 83, 84} be an explicitly enumerated finite set. Does 82 satisfy 82∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"82 occurs in the explicit enumeration of A, so 82∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0010","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ab78e77faf71da990ddb81b03ce53203a2c05602163f07c817172fcd32f021d","family_id":"qf-finite-set-membership","seed":20260942,"semantic_template":"finite-set/unlisted_element/elements-91,92/query-97"},"fields":{"title":"Finite Set Membership","stem":"Let A={91, 92} be an explicitly enumerated finite set. Does 97 satisfy 97∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"97 does not occur in the explicit enumeration of A, so 97∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0011","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8443f6fca76262d0a5875adf4deb7fbb3c457631eb62747ed4eb6159a5b60465","family_id":"qf-finite-set-membership","seed":20260943,"semantic_template":"finite-set/listed_element/elements-101,102,103/query-103"},"fields":{"title":"Finite Set Membership","stem":"Let A={101, 102, 103} be an explicitly enumerated finite set. Does 103 satisfy 103∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"103 occurs in the explicit enumeration of A, so 103∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0012","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7204c5978db404462230500c60c4fd91580f0ac718afc24c26067e0ebf1b50a5","family_id":"qf-finite-set-membership","seed":20260944,"semantic_template":"finite-set/unlisted_element/elements-111,112,113,114/query-119"},"fields":{"title":"Finite Set Membership","stem":"Let A={111, 112, 113, 114} be an explicitly enumerated finite set. Does 119 satisfy 119∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"119 does not occur in the explicit enumeration of A, so 119∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0013","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52c4b0a13d6f2cd8e58c0c14f6650900874b51f0443f0eb5cf90b60806c312f5","family_id":"qf-finite-set-membership","seed":20260945,"semantic_template":"finite-set/listed_element/elements-121,122/query-122"},"fields":{"title":"Finite Set Membership","stem":"Let A={121, 122} be an explicitly enumerated finite set. Does 122 satisfy 122∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"122 occurs in the explicit enumeration of A, so 122∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0014","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6141dff46999201091a4c92d2abec799fc3c75047ac60315b8af755fe33b72e4","family_id":"qf-finite-set-membership","seed":20260946,"semantic_template":"finite-set/unlisted_element/elements-131,132,133/query-138"},"fields":{"title":"Finite Set Membership","stem":"Let A={131, 132, 133} be an explicitly enumerated finite set. Does 138 satisfy 138∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"138 does not occur in the explicit enumeration of A, so 138∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0015","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4500ef153b3b9053dfd11f1dae17ec43b613521618041f4a8034fc6b80aecf95","family_id":"qf-finite-set-membership","seed":20260947,"semantic_template":"finite-set/listed_element/elements-141,142,143,144/query-144"},"fields":{"title":"Finite Set Membership","stem":"Let A={141, 142, 143, 144} be an explicitly enumerated finite set. Does 144 satisfy 144∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"144 occurs in the explicit enumeration of A, so 144∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0016","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6dac57b272ce9c1658a729759a1ce7b25bdf75e0ab143101df322a7510507bae","family_id":"qf-finite-set-membership","seed":20260948,"semantic_template":"finite-set/unlisted_element/elements-151,152/query-157"},"fields":{"title":"Finite Set Membership","stem":"Let A={151, 152} be an explicitly enumerated finite set. Does 157 satisfy 157∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"157 does not occur in the explicit enumeration of A, so 157∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0017","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aeac6d049ec060a2d60d8dafb6044f7520b992c813d16e18c5b0285cf5a12b8f","family_id":"qf-finite-set-membership","seed":20260949,"semantic_template":"finite-set/listed_element/elements-161,162,163/query-163"},"fields":{"title":"Finite Set Membership","stem":"Let A={161, 162, 163} be an explicitly enumerated finite set. Does 163 satisfy 163∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"163 occurs in the explicit enumeration of A, so 163∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0018","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3abce34205d7b4bd329348f1a56a19b0f1e24422776944264544c9f7c0dc1ac0","family_id":"qf-finite-set-membership","seed":20260950,"semantic_template":"finite-set/unlisted_element/elements-171,172,173,174/query-179"},"fields":{"title":"Finite Set Membership","stem":"Let A={171, 172, 173, 174} be an explicitly enumerated finite set. Does 179 satisfy 179∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"179 does not occur in the explicit enumeration of A, so 179∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0019","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c839ebb0f37fa88ace3ade64ab787ab785bb3e233971045fa0ec7bc6efc13143","family_id":"qf-finite-set-membership","seed":20260951,"semantic_template":"finite-set/listed_element/elements-181,182/query-182"},"fields":{"title":"Finite Set Membership","stem":"Let A={181, 182} be an explicitly enumerated finite set. Does 182 satisfy 182∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"182 occurs in the explicit enumeration of A, so 182∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0020","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"90be27aa4fe57fa05f1f42a29e9b11fe7a04bc8f2092f87e31fc03e4076f6369","family_id":"qf-finite-set-membership","seed":20260952,"semantic_template":"finite-set/unlisted_element/elements-191,192,193/query-198"},"fields":{"title":"Finite Set Membership","stem":"Let A={191, 192, 193} be an explicitly enumerated finite set. Does 198 satisfy 198∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"198 does not occur in the explicit enumeration of A, so 198∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0021","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c3e22baae64742b294b6d2963c58e6190aebf58eedbdcfea683c43400ccc4b16","family_id":"qf-finite-set-membership","seed":20260953,"semantic_template":"finite-set/listed_element/elements-201,202,203,204/query-202"},"fields":{"title":"Finite Set Membership","stem":"Let A={201, 202, 203, 204} be an explicitly enumerated finite set. Does 202 satisfy 202∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"202 occurs in the explicit enumeration of A, so 202∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0022","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74c4ab1fcfb693a7d5c4f8b9a83d95b26889c61cbc9e2be905f9c0b3cf1bc8b2","family_id":"qf-finite-set-membership","seed":20260954,"semantic_template":"finite-set/unlisted_element/elements-211,212/query-217"},"fields":{"title":"Finite Set Membership","stem":"Let A={211, 212} be an explicitly enumerated finite set. Does 217 satisfy 217∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"217 does not occur in the explicit enumeration of A, so 217∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0023","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f0f51e6a95f69d5e35a67413adb388b23fc19ba1b69208847f18bbee9133b3d","family_id":"qf-finite-set-membership","seed":20260955,"semantic_template":"finite-set/listed_element/elements-221,222,223/query-223"},"fields":{"title":"Finite Set Membership","stem":"Let A={221, 222, 223} be an explicitly enumerated finite set. Does 223 satisfy 223∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"223 occurs in the explicit enumeration of A, so 223∈A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0024","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"10c7fc7d2cd46fdf6cf7f462c06a2bcec121abe8f634c9adab94daf4311672cc","family_id":"qf-finite-set-membership","seed":20260956,"semantic_template":"finite-set/unlisted_element/elements-231,232,233,234/query-239"},"fields":{"title":"Finite Set Membership","stem":"Let A={231, 232, 233, 234} be an explicitly enumerated finite set. Does 239 satisfy 239∈A?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"239 does not occur in the explicit enumeration of A, so 239∉A."},"skills":["set membership","finite enumeration"],"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-20260913-finite-set-membership-0025","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4fa46110bac74c97fc080d1717e4107c7988d49f54cc09136e94ef12f340bf42","family_id":"qf-finite-set-membership","seed":20260957,"semantic_template":"finite-set/listed_element/elements-241,242/query-242"},"fields":{"title":"Finite Set Membership","stem":"Let A={241, 242} be an explicitly enumerated finite set. Does 242 satisfy 242∈A?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"242 occurs in the explicit enumeration of A, so 242∈A."},"skills":["set membership","finite enumeration"],"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-20260913-proposition-classification-0001","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"261c0fcadcdaad151fcdd932a30e7eef74cca3b477ba9ee44ec753af8f384011","family_id":"qf-proposition-classification","seed":20260958,"semantic_template":"proposition/closed_declarative/membership_constant"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “0 belongs to the N used by this entry.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"It is a closed statement whose truth value can be discussed in the specified classical context. Being a proposition does not mean it has been proved true."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0002","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6095f72f5c8804171345be931ea96d9851bd2095531efe941dedc83244a4815b","family_id":"qf-proposition-classification","seed":20260959,"semantic_template":"proposition/closed_declarative/numeric_identity"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “7=7.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"It is a closed statement whose truth value can be discussed in the specified classical context. Being a proposition does not mean it has been proved true."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0003","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a548af42657509e2388e5bf45fc3c659c856b08329b513f0f2260d92b91505fa","family_id":"qf-proposition-classification","seed":20260960,"semantic_template":"proposition/closed_declarative/numeric_inequality"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “3 is greater than 9.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"It is a closed statement whose truth value can be discussed in the specified classical context. Being a proposition does not mean it has been proved true."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0004","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"32149664e7f75ab8fb4aadf3565d803020524fd27190dcaf0a7b6b1ca85cb590","family_id":"qf-proposition-classification","seed":20260961,"semantic_template":"proposition/closed_declarative/numeric_distinctness"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “0=1.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"It is a closed statement whose truth value can be discussed in the specified classical context. Being a proposition does not mean it has been proved true."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0005","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a75aa643ff12bb834a2f752887f1840d8d3f4c6068e77481a6799767386fc4c9","family_id":"qf-proposition-classification","seed":20260962,"semantic_template":"proposition/closed_declarative/numeric_less_than"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “5 is less than 8.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"It is a closed statement whose truth value can be discussed in the specified classical context. Being a proposition does not mean it has been proved true."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0006","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8605c4aeba59a8790f95b00691877ad05f88644fd9109ea584c176d218bf8e87","family_id":"qf-proposition-classification","seed":20260963,"semantic_template":"proposition/open_sentence/inequality_free_variable"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “x>0.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It contains an unspecified free variable and is therefore an open sentence. It requires assignment, substitution, or quantification before evaluation."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0007","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d825b4f57f9f540eab12b60449c52c74903299bbee28fe0244d727e13a020b64","family_id":"qf-proposition-classification","seed":20260964,"semantic_template":"proposition/open_sentence/parity_predicate_free_variable"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “n is even.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It contains an unspecified free variable and is therefore an open sentence. It requires assignment, substitution, or quantification before evaluation."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0008","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a79ed59e97c4bbcf9c9216008faf099afdf93b2efe89a15a2f240ccba2121914","family_id":"qf-proposition-classification","seed":20260965,"semantic_template":"proposition/open_sentence/membership_free_variable"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “y∈A.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It contains an unspecified free variable and is therefore an open sentence. It requires assignment, substitution, or quantification before evaluation."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0009","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e104d023473f20f3782d6f54cf58076f31209d2cf2a47c853459836198928219","family_id":"qf-proposition-classification","seed":20260966,"semantic_template":"proposition/open_sentence/equation_three_free_variables"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “a+b=c.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It contains an unspecified free variable and is therefore an open sentence. It requires assignment, substitution, or quantification before evaluation."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0010","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fad0defc0942a1dbdf27dcd494fabfb631b883acec2f0987b18a8df511964720","family_id":"qf-proposition-classification","seed":20260967,"semantic_template":"proposition/open_sentence/mapping_free_variables"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “f(x)=y.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It contains an unspecified free variable and is therefore an open sentence. It requires assignment, substitution, or quantification before evaluation."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0011","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d105712cfadc1681633b6e250853ab7ae3700b499a81dbbdd06ecad9c38fb827","family_id":"qf-proposition-classification","seed":20260968,"semantic_template":"proposition/question/comparison_interrogative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Is x greater than 0?” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an interrogative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0012","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c36760e34f4280de0286adc7cd6fd48d7167ec188acdcf8428b7eb5556ba27f8","family_id":"qf-proposition-classification","seed":20260969,"semantic_template":"proposition/question/membership_interrogative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Does 0 belong to N?” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an interrogative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0013","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc1ed4fc516ef2c7c1131f9d4233424a752ba9f96d3d7bc41f4591731b6d9d52","family_id":"qf-proposition-classification","seed":20260970,"semantic_template":"proposition/question/cardinality_interrogative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “How many elements does this set have?” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an interrogative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0014","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48c45ea381791e3e7556e1b0d5b6864555db7a01d6d92b6248b93e56326045ff","family_id":"qf-proposition-classification","seed":20260971,"semantic_template":"proposition/question/function_status_interrogative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Is f a function?” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an interrogative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0015","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d83e826458c4501b8ab0c57b53d4f6e2f3ef1e0d09834a14899480e0b5a00e2","family_id":"qf-proposition-classification","seed":20260972,"semantic_template":"proposition/question/classification_interrogative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Can you classify P?” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an interrogative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0016","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd58c11b96019fec4b417b34fd3146b32011dbe803820d2fd36898db446c3abc","family_id":"qf-proposition-classification","seed":20260973,"semantic_template":"proposition/command/assignment_imperative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Set x to 0.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an imperative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0017","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7398db26947ef943690062cbf5c611ae76b5e453d733016589dd69ba80b3dc25","family_id":"qf-proposition-classification","seed":20260974,"semantic_template":"proposition/command/calculation_imperative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Calculate this distance.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an imperative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0018","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e5be7ddaa2bf856f0f23c4df1f508a81049ec85095f10aae5966a90ecbc09a41","family_id":"qf-proposition-classification","seed":20260975,"semantic_template":"proposition/command/collection_imperative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Find the elements of set A.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an imperative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0019","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c07fa61f01f314186114e8e07e49cd4b2901a173beffd631d0715419d3dba733","family_id":"qf-proposition-classification","seed":20260976,"semantic_template":"proposition/command/proof_imperative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Prove P.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an imperative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0020","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6ebbe2ef73d54342ba7fd66f037c7b415c1a7a7f19cb90fde93930828cb2365c","family_id":"qf-proposition-classification","seed":20260977,"semantic_template":"proposition/command/mapping_imperative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Map the input into Y.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an imperative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0021","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8a253f3a43babbf6e439769baf9311c2845d6971729c9404f5da86b185874b0","family_id":"qf-proposition-classification","seed":20260978,"semantic_template":"proposition/closed_declarative/universal_reflexivity"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Every number equals itself.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"It is a closed statement whose truth value can be discussed in the specified classical context. Being a proposition does not mean it has been proved true."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0022","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1eef229dbc70f77cbdf65ce8f3eabf2020e211180d4abac625c08fd0fc880dc5","family_id":"qf-proposition-classification","seed":20260979,"semantic_template":"proposition/open_sentence/successor_equation_free_variable"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “z+1=4.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It contains an unspecified free variable and is therefore an open sentence. It requires assignment, substitution, or quantification before evaluation."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0023","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7d3cc0ade4620d0dc1a35ab893bf9ed374b491d08ea4a3cac503f66e13c10fe1","family_id":"qf-proposition-classification","seed":20260980,"semantic_template":"proposition/question/provability_interrogative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Has P been proved?” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an interrogative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0024","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"654a5d2747a4828cec8a1bfc725fb54518ff993fcd2eabbbeff539a926127aa2","family_id":"qf-proposition-classification","seed":20260981,"semantic_template":"proposition/command/logic_boundary_imperative"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “Do not treat P as proved.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"It is an imperative sentence rather than a closed statement that is directly asserted or denied."},"skills":["proposition classification","sentence closure"],"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-20260913-proposition-classification-0025","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d446d1e393f5aad50627cb2b366522dff08bc0c8c8fb12da254fb6cdfb964b4f","family_id":"qf-proposition-classification","seed":20260982,"semantic_template":"proposition/closed_declarative/existential_identity"},"fields":{"title":"Proposition Classification","stem":"In the introductory classical-logic context specified here, is “There exists a number equal to 0.” a proposition? Classify it only; do not decide its truth or proof status.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"It is a closed statement whose truth value can be discussed in the specified classical context. Being a proposition does not mean it has been proved true."},"skills":["proposition classification","sentence closure"],"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-20260913-finite-function-mapping-0001","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9332e33f0d38275ba282f3cee52bd25f87c34b18f039b70ed6358921dbd799b9","family_id":"qf-finite-function-mapping","seed":20260983,"semantic_template":"function/valid/domain-4/pairs-0>0;1>0;2>0;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x1-1, x1-2, x1-3, x1-4} and Y={y1-1, y1-2, y1-3, y1-4, y1-5}. The finite correspondence is x1-1↦y1-1, x1-2↦y1-1, x1-3↦y1-1, x1-4↦y1-1. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every input in X has exactly one output, and every output belongs to Y. The actual range may be a proper subset of Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0002","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8568106b7fdc5aed016593923d90ed9184ea717de534944b9166ede301601a7b","family_id":"qf-finite-function-mapping","seed":20260984,"semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;0>1;1>0;2>0;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x2-1, x2-2, x2-3, x2-4} and Y={y2-1, y2-2, y2-3, y2-4, y2-5}. The finite correspondence is x2-1↦y2-1, x2-2↦y2-1, x2-3↦y2-1, x2-4↦y2-1, x2-1↦y2-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input is assigned more than one output, so the correspondence is not a function."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0003","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"707f7fad6289ffbfc05f8a06bd3339b709cf03d6894ea13807716f3a89eee52e","family_id":"qf-finite-function-mapping","seed":20260985,"semantic_template":"function/missing_input/domain-4/pairs-1>0;2>0;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x3-1, x3-2, x3-3, x3-4} and Y={y3-1, y3-2, y3-3, y3-4, y3-5}. The finite correspondence is x3-2↦y3-1, x3-3↦y3-1, x3-4↦y3-1. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input in X has no assigned output, so the correspondence is not a total function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0004","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca7708dddeed4ffbe7cdb8abcdf591e1fad4793168f92fd02645a3d132469669","family_id":"qf-finite-function-mapping","seed":20260986,"semantic_template":"function/outside_codomain/domain-4/pairs-0>-1;1>0;2>0;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x4-1, x4-2, x4-3, x4-4} and Y={y4-1, y4-2, y4-3, y4-4, y4-5}. The finite correspondence is x4-1↦z4, x4-2↦y4-1, x4-3↦y4-1, x4-4↦y4-1. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one assigned output lies outside the declared codomain Y, so the correspondence does not define a function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0005","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f51a44ca6d4687d8a1416c148495ee60c0bccfce9a3113cc9586e93c26605eac","family_id":"qf-finite-function-mapping","seed":20260987,"semantic_template":"function/valid/domain-4/pairs-0>0;1>0;2>0;3>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x5-1, x5-2, x5-3, x5-4} and Y={y5-1, y5-2, y5-3, y5-4, y5-5}. The finite correspondence is x5-1↦y5-1, x5-2↦y5-1, x5-3↦y5-1, x5-4↦y5-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every input in X has exactly one output, and every output belongs to Y. The actual range may be a proper subset of Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0006","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7fd101cd470aa12c79b0719113f46b8b3327d0e404a54ba979647ced24f6b2fa","family_id":"qf-finite-function-mapping","seed":20260988,"semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>0;1>1;2>0;3>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x6-1, x6-2, x6-3, x6-4} and Y={y6-1, y6-2, y6-3, y6-4, y6-5}. The finite correspondence is x6-1↦y6-1, x6-2↦y6-1, x6-3↦y6-1, x6-4↦y6-2, x6-2↦y6-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input is assigned more than one output, so the correspondence is not a function."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0007","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3ee27c2cc2509e4f601da4b831e140592b53df93802659580eaf476e1f61dd66","family_id":"qf-finite-function-mapping","seed":20260989,"semantic_template":"function/missing_input/domain-4/pairs-0>0;2>0;3>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x7-1, x7-2, x7-3, x7-4} and Y={y7-1, y7-2, y7-3, y7-4, y7-5}. The finite correspondence is x7-1↦y7-1, x7-3↦y7-1, x7-4↦y7-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input in X has no assigned output, so the correspondence is not a total function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0008","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b011af113cef4199563e14222082fb93967e376a76e7c5f1415a6515e956d2f8","family_id":"qf-finite-function-mapping","seed":20260990,"semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>-1;2>0;3>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x8-1, x8-2, x8-3, x8-4} and Y={y8-1, y8-2, y8-3, y8-4, y8-5}. The finite correspondence is x8-1↦y8-1, x8-2↦z8, x8-3↦y8-1, x8-4↦y8-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one assigned output lies outside the declared codomain Y, so the correspondence does not define a function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0009","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6f55079bf907df6377892d3c3f6235bdd45f978855b51fa8ce40b4745bc292c6","family_id":"qf-finite-function-mapping","seed":20260991,"semantic_template":"function/valid/domain-4/pairs-0>0;1>0;2>1;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x9-1, x9-2, x9-3, x9-4} and Y={y9-1, y9-2, y9-3, y9-4, y9-5}. The finite correspondence is x9-1↦y9-1, x9-2↦y9-1, x9-3↦y9-2, x9-4↦y9-1. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every input in X has exactly one output, and every output belongs to Y. The actual range may be a proper subset of Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0010","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6ff974dffce850d892e92a1878cd4470e35a429a420b8b6f0450b459e4c97c4","family_id":"qf-finite-function-mapping","seed":20260992,"semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>0;2>1;2>2;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x10-1, x10-2, x10-3, x10-4} and Y={y10-1, y10-2, y10-3, y10-4, y10-5}. The finite correspondence is x10-1↦y10-1, x10-2↦y10-1, x10-3↦y10-2, x10-4↦y10-1, x10-3↦y10-3. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input is assigned more than one output, so the correspondence is not a function."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0011","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87429ddcbb4eda22b15e149171bd8b42edd63ae51a5af1d42a66ac71e7080658","family_id":"qf-finite-function-mapping","seed":20260993,"semantic_template":"function/missing_input/domain-4/pairs-0>0;1>0;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x11-1, x11-2, x11-3, x11-4} and Y={y11-1, y11-2, y11-3, y11-4, y11-5}. The finite correspondence is x11-1↦y11-1, x11-2↦y11-1, x11-4↦y11-1. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input in X has no assigned output, so the correspondence is not a total function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0012","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"328e996ee27e458e2127e7f782512baf788d48e1e2a46d04efdad5fc81f85d66","family_id":"qf-finite-function-mapping","seed":20260994,"semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>0;2>-1;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x12-1, x12-2, x12-3, x12-4} and Y={y12-1, y12-2, y12-3, y12-4, y12-5}. The finite correspondence is x12-1↦y12-1, x12-2↦y12-1, x12-3↦z12, x12-4↦y12-1. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one assigned output lies outside the declared codomain Y, so the correspondence does not define a function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0013","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e7527b52d0b3bbdc0d05a82ef5de3b6eaee2b98f9449b5fcbe686cd7eef327c1","family_id":"qf-finite-function-mapping","seed":20260995,"semantic_template":"function/valid/domain-4/pairs-0>0;1>0;2>1;3>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x13-1, x13-2, x13-3, x13-4} and Y={y13-1, y13-2, y13-3, y13-4, y13-5}. The finite correspondence is x13-1↦y13-1, x13-2↦y13-1, x13-3↦y13-2, x13-4↦y13-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every input in X has exactly one output, and every output belongs to Y. The actual range may be a proper subset of Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0014","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"01d2c001828fd07aa2302f41c6d8bfeb3d2cd84450dd821d5759a54781eb626b","family_id":"qf-finite-function-mapping","seed":20260996,"semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>0;2>1;3>1;3>2"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x14-1, x14-2, x14-3, x14-4} and Y={y14-1, y14-2, y14-3, y14-4, y14-5}. The finite correspondence is x14-1↦y14-1, x14-2↦y14-1, x14-3↦y14-2, x14-4↦y14-2, x14-4↦y14-3. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input is assigned more than one output, so the correspondence is not a function."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0015","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aa97661ed2ea7fd0a68363e5cc0c0b036980e03f2dedb1b4ac50da81989d8d8d","family_id":"qf-finite-function-mapping","seed":20260997,"semantic_template":"function/missing_input/domain-4/pairs-0>0;1>0;2>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x15-1, x15-2, x15-3, x15-4} and Y={y15-1, y15-2, y15-3, y15-4, y15-5}. The finite correspondence is x15-1↦y15-1, x15-2↦y15-1, x15-3↦y15-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input in X has no assigned output, so the correspondence is not a total function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0016","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b78bc9d5e96d0fd755f9f68153934d5d4ea00a9cb895999a779fb8e2c81db85","family_id":"qf-finite-function-mapping","seed":20260998,"semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>0;2>1;3>-1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x16-1, x16-2, x16-3, x16-4} and Y={y16-1, y16-2, y16-3, y16-4, y16-5}. The finite correspondence is x16-1↦y16-1, x16-2↦y16-1, x16-3↦y16-2, x16-4↦z16. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one assigned output lies outside the declared codomain Y, so the correspondence does not define a function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0017","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"14e8578dc27903e92591ce51e2f6660921f4278c013580835e76d2b5e5e8221d","family_id":"qf-finite-function-mapping","seed":20260999,"semantic_template":"function/valid/domain-4/pairs-0>0;1>0;2>1;3>2"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x17-1, x17-2, x17-3, x17-4} and Y={y17-1, y17-2, y17-3, y17-4, y17-5}. The finite correspondence is x17-1↦y17-1, x17-2↦y17-1, x17-3↦y17-2, x17-4↦y17-3. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every input in X has exactly one output, and every output belongs to Y. The actual range may be a proper subset of Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0018","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b759a18a370c201ef2865e670452ee76b55eab37ae155861c07a1433e1f2f52e","family_id":"qf-finite-function-mapping","seed":20261000,"semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;0>1;1>0;2>1;3>2"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x18-1, x18-2, x18-3, x18-4} and Y={y18-1, y18-2, y18-3, y18-4, y18-5}. The finite correspondence is x18-1↦y18-1, x18-2↦y18-1, x18-3↦y18-2, x18-4↦y18-3, x18-1↦y18-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input is assigned more than one output, so the correspondence is not a function."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0019","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"17d110e9f79cf99ba49ccc7f71a0046153d1d441cd6b53cab922842fcf049913","family_id":"qf-finite-function-mapping","seed":20261001,"semantic_template":"function/missing_input/domain-4/pairs-1>0;2>1;3>2"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x19-1, x19-2, x19-3, x19-4} and Y={y19-1, y19-2, y19-3, y19-4, y19-5}. The finite correspondence is x19-2↦y19-1, x19-3↦y19-2, x19-4↦y19-3. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input in X has no assigned output, so the correspondence is not a total function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0020","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8fde63a7447634764469b82119229b2bf4a80f8bd03851f4d0de5fb6b50eec12","family_id":"qf-finite-function-mapping","seed":20261002,"semantic_template":"function/outside_codomain/domain-4/pairs-0>-1;1>0;2>1;3>2"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x20-1, x20-2, x20-3, x20-4} and Y={y20-1, y20-2, y20-3, y20-4, y20-5}. The finite correspondence is x20-1↦z20, x20-2↦y20-1, x20-3↦y20-2, x20-4↦y20-3. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one assigned output lies outside the declared codomain Y, so the correspondence does not define a function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0021","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e726295362234e04e697bc7449d24307d539df6c6dff5847f6fd8bc4b00a9ae6","family_id":"qf-finite-function-mapping","seed":20261003,"semantic_template":"function/valid/domain-4/pairs-0>0;1>1;2>0;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x21-1, x21-2, x21-3, x21-4} and Y={y21-1, y21-2, y21-3, y21-4, y21-5}. The finite correspondence is x21-1↦y21-1, x21-2↦y21-2, x21-3↦y21-1, x21-4↦y21-1. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every input in X has exactly one output, and every output belongs to Y. The actual range may be a proper subset of Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0022","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f1983632199bdb6b17044e22de118a05e8483dfcc0a9cafa66d6dabf0156e9f9","family_id":"qf-finite-function-mapping","seed":20261004,"semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>1;1>2;2>0;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x22-1, x22-2, x22-3, x22-4} and Y={y22-1, y22-2, y22-3, y22-4, y22-5}. The finite correspondence is x22-1↦y22-1, x22-2↦y22-2, x22-3↦y22-1, x22-4↦y22-1, x22-2↦y22-3. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input is assigned more than one output, so the correspondence is not a function."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0023","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0a53ded1be4ab4fdcff8fc57ff3afde606c19fea7c0a147f1ef5d55bce60aa58","family_id":"qf-finite-function-mapping","seed":20261005,"semantic_template":"function/missing_input/domain-4/pairs-0>0;2>0;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x23-1, x23-2, x23-3, x23-4} and Y={y23-1, y23-2, y23-3, y23-4, y23-5}. The finite correspondence is x23-1↦y23-1, x23-3↦y23-1, x23-4↦y23-1. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input in X has no assigned output, so the correspondence is not a total function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0024","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a379457673ddea7742a5e8885d44694b46831a8d9e58c6df5a2170f9e9b7324","family_id":"qf-finite-function-mapping","seed":20261006,"semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>-1;2>0;3>0"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x24-1, x24-2, x24-3, x24-4} and Y={y24-1, y24-2, y24-3, y24-4, y24-5}. The finite correspondence is x24-1↦y24-1, x24-2↦z24, x24-3↦y24-1, x24-4↦y24-1. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one assigned output lies outside the declared codomain Y, so the correspondence does not define a function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0025","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2471e120a29ce63da13dcd22bb161d13d5f12aacc5cecaa9e1a0a0faa5283c1c","family_id":"qf-finite-function-mapping","seed":20261007,"semantic_template":"function/valid/domain-4/pairs-0>0;1>1;2>0;3>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x25-1, x25-2, x25-3, x25-4} and Y={y25-1, y25-2, y25-3, y25-4, y25-5}. The finite correspondence is x25-1↦y25-1, x25-2↦y25-2, x25-3↦y25-1, x25-4↦y25-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every input in X has exactly one output, and every output belongs to Y. The actual range may be a proper subset of Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0026","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ffaa53c131d5dc4a914a17401e41b03b499469b55c14e967f89cdeb458cabc30","family_id":"qf-finite-function-mapping","seed":20261008,"semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>1;2>0;2>1;3>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x26-1, x26-2, x26-3, x26-4} and Y={y26-1, y26-2, y26-3, y26-4, y26-5}. The finite correspondence is x26-1↦y26-1, x26-2↦y26-2, x26-3↦y26-1, x26-4↦y26-2, x26-3↦y26-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input is assigned more than one output, so the correspondence is not a function."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0027","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64aaeb3cdbc01e5763a828d0eb9c510a56262ed5a9b51569ea23af379195e1bf","family_id":"qf-finite-function-mapping","seed":20261009,"semantic_template":"function/missing_input/domain-4/pairs-0>0;1>1;3>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x27-1, x27-2, x27-3, x27-4} and Y={y27-1, y27-2, y27-3, y27-4, y27-5}. The finite correspondence is x27-1↦y27-1, x27-2↦y27-2, x27-4↦y27-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input in X has no assigned output, so the correspondence is not a total function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0028","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c33b84b5fb4888b2185623febbce11867776e95e50812c1e52ab30b3b5ac4b0c","family_id":"qf-finite-function-mapping","seed":20261010,"semantic_template":"function/outside_codomain/domain-4/pairs-0>0;1>1;2>-1;3>1"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x28-1, x28-2, x28-3, x28-4} and Y={y28-1, y28-2, y28-3, y28-4, y28-5}. The finite correspondence is x28-1↦y28-1, x28-2↦y28-2, x28-3↦z28, x28-4↦y28-2. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one assigned output lies outside the declared codomain Y, so the correspondence does not define a function X→Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0029","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4871149fee2e518155f60b9e88655b12c674501f420604313eb0999533084cfc","family_id":"qf-finite-function-mapping","seed":20261011,"semantic_template":"function/valid/domain-4/pairs-0>0;1>1;2>0;3>2"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x29-1, x29-2, x29-3, x29-4} and Y={y29-1, y29-2, y29-3, y29-4, y29-5}. The finite correspondence is x29-1↦y29-1, x29-2↦y29-2, x29-3↦y29-1, x29-4↦y29-3. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every input in X has exactly one output, and every output belongs to Y. The actual range may be a proper subset of Y."},"skills":["function definition","domain and codomain"],"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-20260913-finite-function-mapping-0030","batch_id":"batch-20260913-foundational-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"be6bf0812e003debd925b37702e3480efda8fca379fcc4a4cfd9e0224581e168","family_id":"qf-finite-function-mapping","seed":20261012,"semantic_template":"function/multiple_outputs/domain-4/pairs-0>0;1>1;2>0;3>2;3>3"},"fields":{"title":"Finite Mapping as a Function","stem":"Let X={x30-1, x30-2, x30-3, x30-4} and Y={y30-1, y30-2, y30-3, y30-4, y30-5}. The finite correspondence is x30-1↦y30-1, x30-2↦y30-2, x30-3↦y30-1, x30-4↦y30-3, x30-4↦y30-4. Does it define a function f:X→Y? Keep the codomain Y distinct from the actual range.","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"At least one input is assigned more than one output, so the correspondence is not a function."},"skills":["function definition","domain and codomain"],"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."}}