{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r04-set-0001","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df83dedc56811a7e9459c048fef29ffeada2d1c7f72d2f755aa87f649337b5e8","family_id":"qf-density11-set-normalized-enumeration","seed":202610114001,"semantic_template":"qf-density11-set-normalized-enumeration/[]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is []."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0002","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c316391a8546eac3d19e35272fcd21bc301c2453672b5fd083c94ed5829b0ffe","family_id":"qf-density11-set-normalized-enumeration","seed":202610114002,"semantic_template":"qf-density11-set-normalized-enumeration/[0]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[0, 0]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[0]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [0]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0003","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f2be0a67e00a7b9c14e9333a98e699edc8e113c764a7cf30e9caf868862209e","family_id":"qf-density11-set-normalized-enumeration","seed":202610114003,"semantic_template":"qf-density11-set-normalized-enumeration/[-2,1]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[-2, 1, -2]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-2, 1]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-2, 1]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0004","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f1430ffaf503ec058df4ac9dcbb57c8bac168b01c7bb853af0bd00655482671c","family_id":"qf-density11-set-normalized-enumeration","seed":202610114004,"semantic_template":"qf-density11-set-normalized-enumeration/[-3,0,3]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[3, -3, 0, 3]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-3, 0, 3]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-3, 0, 3]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0005","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9101aa5b4f1faafc765e085d556cfb6ea10fd5595d1d43f892a64b12f21f047","family_id":"qf-density11-set-normalized-enumeration","seed":202610114005,"semantic_template":"qf-density11-set-normalized-enumeration/[-4,0,4]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[4, -4, 0, 4]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-4, 0, 4]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-4, 0, 4]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0006","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c65ef9c6ca584056f6289b58487b7618fe3f68ed4877fd0136f339edd836ac7","family_id":"qf-density11-set-normalized-enumeration","seed":202610114006,"semantic_template":"qf-density11-set-normalized-enumeration/[-5,0,5]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[5, -5, 0, 5]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-5, 0, 5]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-5, 0, 5]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0007","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e839249ae48b8505af8f1f6a743382cdd265701e86714791c1cedf0cc1fb38e0","family_id":"qf-density11-set-normalized-enumeration","seed":202610114007,"semantic_template":"qf-density11-set-normalized-enumeration/[-6,0,6]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[6, -6, 0, 6]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-6, 0, 6]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-6, 0, 6]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0008","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5ec008513c45783e82979455be7144d49b62ea2ad761194e8b01e095b6a30c7","family_id":"qf-density11-set-normalized-enumeration","seed":202610114008,"semantic_template":"qf-density11-set-normalized-enumeration/[-7,0,7]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[7, -7, 0, 7]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-7, 0, 7]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-7, 0, 7]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0009","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b06554debe0ee0cc8414cefde9cccb654ea5559a13108b756028f4bbb5d7d56b","family_id":"qf-density11-set-normalized-enumeration","seed":202610114009,"semantic_template":"qf-density11-set-normalized-enumeration/[-8,0,8]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[8, -8, 0, 8]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-8, 0, 8]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-8, 0, 8]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0010","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0a1a0dfec64c67456ff0f4bed2be5d6db98b0f2819ee81e9eb0eba5962a55263","family_id":"qf-density11-set-normalized-enumeration","seed":202610114010,"semantic_template":"qf-density11-set-normalized-enumeration/[-9,0,9]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[9, -9, 0, 9]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-9, 0, 9]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-9, 0, 9]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0011","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81b0f17b8d033f693816f93d1aa25bc9b4b93e48edb688004f540eaeffb19317","family_id":"qf-density11-set-normalized-enumeration","seed":202610114011,"semantic_template":"qf-density11-set-normalized-enumeration/[-10,0,10]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[10, -10, 0, 10]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-10, 0, 10]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-10, 0, 10]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0012","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74bb39869b4923eb60ce734474f62bf78c7ddd0214bf8998934742f50e2a13b4","family_id":"qf-density11-set-normalized-enumeration","seed":202610114012,"semantic_template":"qf-density11-set-normalized-enumeration/[-11,0,11]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[11, -11, 0, 11]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-11, 0, 11]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-11, 0, 11]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0013","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8374ffd0eca8c37bddb0d6ce003f7278d10f7a116843fc714d25ebde3fb42c37","family_id":"qf-density11-set-normalized-enumeration","seed":202610114013,"semantic_template":"qf-density11-set-normalized-enumeration/[-12,0,12]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[12, -12, 0, 12]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-12, 0, 12]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-12, 0, 12]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0014","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"07d7adfb469fa4dc7bdb1af8ccd4410abe17fd0c8c464ff979fc7c78426843b0","family_id":"qf-density11-set-normalized-enumeration","seed":202610114014,"semantic_template":"qf-density11-set-normalized-enumeration/[-13,0,13]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[13, -13, 0, 13]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-13, 0, 13]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-13, 0, 13]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0015","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7fb94512af6f6a067416aa42dc088a63508182d302bf01b12682562dbbecb8b4","family_id":"qf-density11-set-normalized-enumeration","seed":202610114015,"semantic_template":"qf-density11-set-normalized-enumeration/[-14,0,14]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[14, -14, 0, 14]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-14, 0, 14]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-14, 0, 14]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0016","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b6d41ff6c813265a83f0e50b94db411d906a6fa1df152ee579dd39b7a0bcfa22","family_id":"qf-density11-set-normalized-enumeration","seed":202610114016,"semantic_template":"qf-density11-set-normalized-enumeration/[-15,0,15]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[15, -15, 0, 15]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-15, 0, 15]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-15, 0, 15]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0017","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f1e374e67c48f468ef249f809aade6b1985c2849e2a5360a4afccb8ac7ed6ae9","family_id":"qf-density11-set-normalized-enumeration","seed":202610114017,"semantic_template":"qf-density11-set-normalized-enumeration/[-16,0,16]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[16, -16, 0, 16]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-16, 0, 16]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-16, 0, 16]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0018","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2796192de9dd77d977fd37f7e6a51fe0f747e2fc60ab1ead4d166357adf8a351","family_id":"qf-density11-set-normalized-enumeration","seed":202610114018,"semantic_template":"qf-density11-set-normalized-enumeration/[-17,0,17]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[17, -17, 0, 17]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-17, 0, 17]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-17, 0, 17]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0019","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"304b7d07fdcfac4efcebbd47ed316b3e90471e47e647305961e433d17d49f522","family_id":"qf-density11-set-normalized-enumeration","seed":202610114019,"semantic_template":"qf-density11-set-normalized-enumeration/[-18,0,18]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[18, -18, 0, 18]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-18, 0, 18]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-18, 0, 18]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0020","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3bb663d23750b2e810c787545276a4a6250c9534fe00c20ae5624682b98a906c","family_id":"qf-density11-set-normalized-enumeration","seed":202610114020,"semantic_template":"qf-density11-set-normalized-enumeration/[-19,0,19]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[19, -19, 0, 19]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-19, 0, 19]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-19, 0, 19]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0021","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c1ef11fa5f6406762d0142322f70a5001b20606a5c0de315cc0383077d59decf","family_id":"qf-density11-set-normalized-enumeration","seed":202610114021,"semantic_template":"qf-density11-set-normalized-enumeration/[-20,0,20]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[20, -20, 0, 20]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-20, 0, 20]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-20, 0, 20]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0022","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f729ebb28c70507355b9586f0bc4d3f43631a5161ac4d496fc2188e6c778afb6","family_id":"qf-density11-set-normalized-enumeration","seed":202610114022,"semantic_template":"qf-density11-set-normalized-enumeration/[-21,0,21]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[21, -21, 0, 21]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-21, 0, 21]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-21, 0, 21]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0023","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1fb442023fbd1a45b02d22c8d0d3f44296ee54d278cd8430537b02126693811","family_id":"qf-density11-set-normalized-enumeration","seed":202610114023,"semantic_template":"qf-density11-set-normalized-enumeration/[-22,0,22]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[22, -22, 0, 22]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-22, 0, 22]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-22, 0, 22]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0024","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4c09a432a65eae4600eec0113fe81488062589eae68692ce4b5bc7a5f213b6a","family_id":"qf-density11-set-normalized-enumeration","seed":202610114024,"semantic_template":"qf-density11-set-normalized-enumeration/[-23,0,23]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[23, -23, 0, 23]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-23, 0, 23]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-23, 0, 23]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0025","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8a20ade07fdd506f6dd8fca85d0a686395fbd36ae87ba67d0eca8c4edca3915","family_id":"qf-density11-set-normalized-enumeration","seed":202610114025,"semantic_template":"qf-density11-set-normalized-enumeration/[-24,0,24]"},"fields":{"title":"Normalized Finite Set Enumeration","stem":"The raw integer list is entries=[24, -24, 0, 24]. Remove duplicates and enumerate every set element increasingly, using [] for the empty set.","answer":{"kind":"expression","value":"[-24, 0, 24]","explanation":"Set extension depends on elements, not input order or repetition; list each element once. The exact result, retaining the requested order, is [-24, 0, 24]."},"skills":["Normalized Finite Set 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-20261008-advance-20261011-r04-set-0026","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3a1cc10b1e45689ee505df4ef62602ed3e46b319f5cb839fda749a5b41678e3b","family_id":"qf-density11-set-equality-defect","seed":202610114026,"semantic_template":"qf-density11-set-equality-defect/[[],[]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[0, 1] and B=[1, 0, 1]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(Yes, [], [])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (Yes, [], [])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0027","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c35df2cebc48947e1c63c14bb2d0b7fece4da34b493a7692c2552e10994ad1d","family_id":"qf-density11-set-equality-defect","seed":202610114027,"semantic_template":"qf-density11-set-equality-defect/[[],[-1]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[] and B=[-1]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [], [-1])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [], [-1])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0028","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9194c97fb3234bcd8a3c4592d6b666c9bc063b88b80f09e4a97caf26e2af0127","family_id":"qf-density11-set-equality-defect","seed":202610114028,"semantic_template":"qf-density11-set-equality-defect/[[-2],[]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-2] and B=[]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-2], [])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-2], [])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0029","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"de171cdb225b12b44e2004e11ffc6093fa40a12f3eb3e40976df65bf1e21b11e","family_id":"qf-density11-set-equality-defect","seed":202610114029,"semantic_template":"qf-density11-set-equality-defect/[[-3],[4]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-3, 0, 3] and B=[0, 3, 4]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-3], [4])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-3], [4])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0030","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23d9bdb51359bccda43471d2a669d3977f0df0bf247ff560f82ff08b7202c870","family_id":"qf-density11-set-equality-defect","seed":202610114030,"semantic_template":"qf-density11-set-equality-defect/[[-4],[5]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-4, 0, 4] and B=[0, 4, 5]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-4], [5])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-4], [5])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0031","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f1fe86f05963ea02b0e665ce6cb212caf2e74830d94f3f20e352613a75f6012","family_id":"qf-density11-set-equality-defect","seed":202610114031,"semantic_template":"qf-density11-set-equality-defect/[[-5],[6]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-5, 0, 5] and B=[0, 5, 6]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-5], [6])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-5], [6])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0032","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b962afd7603a780311ae80ded34dcce9a2a68606525e6c1b782ead6e121a02c7","family_id":"qf-density11-set-equality-defect","seed":202610114032,"semantic_template":"qf-density11-set-equality-defect/[[-6],[7]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-6, 0, 6] and B=[0, 6, 7]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-6], [7])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-6], [7])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0033","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cccbb78c1a51f80926bfaf0dbadd7e68c5f09a6f160d7b56c83f2fa9179741b7","family_id":"qf-density11-set-equality-defect","seed":202610114033,"semantic_template":"qf-density11-set-equality-defect/[[-7],[8]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-7, 0, 7] and B=[0, 7, 8]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-7], [8])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-7], [8])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0034","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ec56b89962877dd5727571f01bff2e33358160e41c3cb3f3bdc67dc9dc72d74","family_id":"qf-density11-set-equality-defect","seed":202610114034,"semantic_template":"qf-density11-set-equality-defect/[[-8],[9]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-8, 0, 8] and B=[0, 8, 9]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-8], [9])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-8], [9])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0035","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bfb9c0c1ba4de22fa4748881dd9106946538f99aff9d946118a98f212fcbf308","family_id":"qf-density11-set-equality-defect","seed":202610114035,"semantic_template":"qf-density11-set-equality-defect/[[-9],[10]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-9, 0, 9] and B=[0, 9, 10]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-9], [10])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-9], [10])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0036","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92475e9eece2d6f9949772985386bf8e4dd3ae3cec7b0bff074aee4e38105bbf","family_id":"qf-density11-set-equality-defect","seed":202610114036,"semantic_template":"qf-density11-set-equality-defect/[[-10],[11]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-10, 0, 10] and B=[0, 10, 11]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-10], [11])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-10], [11])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0037","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"191ba5e5e996bb2ad0e23f47fc3379d3c40d136afaf0c277c6b88386136072e4","family_id":"qf-density11-set-equality-defect","seed":202610114037,"semantic_template":"qf-density11-set-equality-defect/[[-11],[12]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-11, 0, 11] and B=[0, 11, 12]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-11], [12])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-11], [12])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0038","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9164a3860fadacd3f8494dfbc228da8e10d63016d6d0281bf4d8ee4947e441cb","family_id":"qf-density11-set-equality-defect","seed":202610114038,"semantic_template":"qf-density11-set-equality-defect/[[-12],[13]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-12, 0, 12] and B=[0, 12, 13]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-12], [13])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-12], [13])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0039","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"83e5b4a9f01de70fd006d75afa9e5a567fa2253b9a1d5a24fba9ccd658fd7e59","family_id":"qf-density11-set-equality-defect","seed":202610114039,"semantic_template":"qf-density11-set-equality-defect/[[-13],[14]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-13, 0, 13] and B=[0, 13, 14]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-13], [14])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-13], [14])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0040","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a7db31b10be27a1917bf5cf1d599f43ee00a96aa3fbc1a91413abac12697b1a3","family_id":"qf-density11-set-equality-defect","seed":202610114040,"semantic_template":"qf-density11-set-equality-defect/[[-14],[15]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-14, 0, 14] and B=[0, 14, 15]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-14], [15])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-14], [15])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0041","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e8654af7c4c90638b6fc13034a7e5ad78196560e9c1277d024e73db433e3047b","family_id":"qf-density11-set-equality-defect","seed":202610114041,"semantic_template":"qf-density11-set-equality-defect/[[-15],[16]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-15, 0, 15] and B=[0, 15, 16]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-15], [16])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-15], [16])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0042","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7394438f123a827025885a2ad74156f2085b82d3955d40da012ddaf65a7de5a5","family_id":"qf-density11-set-equality-defect","seed":202610114042,"semantic_template":"qf-density11-set-equality-defect/[[-16],[17]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-16, 0, 16] and B=[0, 16, 17]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-16], [17])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-16], [17])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0043","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c788c0db9f6bfe1a88c117a50f95f0f1c667856da84307673b7ef0ecb65322d8","family_id":"qf-density11-set-equality-defect","seed":202610114043,"semantic_template":"qf-density11-set-equality-defect/[[-17],[18]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-17, 0, 17] and B=[0, 17, 18]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-17], [18])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-17], [18])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0044","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df0d207d076a577e29ca2edeb140f34fb3e82d477cf574490e2c8b0ca8a38a9a","family_id":"qf-density11-set-equality-defect","seed":202610114044,"semantic_template":"qf-density11-set-equality-defect/[[-18],[19]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-18, 0, 18] and B=[0, 18, 19]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-18], [19])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-18], [19])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0045","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5659561e3387063d90e97919fdf596dc4178c2e44c4a19b7ab23b27b0f78826d","family_id":"qf-density11-set-equality-defect","seed":202610114045,"semantic_template":"qf-density11-set-equality-defect/[[-19],[20]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-19, 0, 19] and B=[0, 19, 20]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-19], [20])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-19], [20])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0046","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df28c2a862e0f5f65fbd24e34858d50cad4b8350609bcd8e829a89914f699e5d","family_id":"qf-density11-set-equality-defect","seed":202610114046,"semantic_template":"qf-density11-set-equality-defect/[[-20],[21]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-20, 0, 20] and B=[0, 20, 21]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-20], [21])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-20], [21])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0047","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a2797b7a7c2a2fb7b9e8ee26caf8ebaf998d97157d28c6ed323d62fe25dcd789","family_id":"qf-density11-set-equality-defect","seed":202610114047,"semantic_template":"qf-density11-set-equality-defect/[[-21],[22]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-21, 0, 21] and B=[0, 21, 22]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-21], [22])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-21], [22])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0048","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"17b7b958fb550ddcab5de6eac0492422c304bf5f9fa704b61a59ab0d431332b0","family_id":"qf-density11-set-equality-defect","seed":202610114048,"semantic_template":"qf-density11-set-equality-defect/[[-22],[23]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-22, 0, 22] and B=[0, 22, 23]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-22], [23])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-22], [23])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0049","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9132455bbe083724082ae21fcc3009fe742f1a9f86fb325a8871a85a43123cf9","family_id":"qf-density11-set-equality-defect","seed":202610114049,"semantic_template":"qf-density11-set-equality-defect/[[-23],[24]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-23, 0, 23] and B=[0, 23, 24]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-23], [24])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-23], [24])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0050","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7641ded83af6eb0b257026219cf602d70c4f188b904ef2bbc498e3c19497bb6","family_id":"qf-density11-set-equality-defect","seed":202610114050,"semantic_template":"qf-density11-set-equality-defect/[[-24],[25]]"},"fields":{"title":"Set Equality with Both Difference Witnesses","stem":"Finite integer sets A=[-24, 0, 24] and B=[0, 24, 25]; repeated elements count once. Give (are A and B equal?, A\\B, B\\A), with increasing difference lists.","answer":{"kind":"expression","value":"(No, [-24], [25])","explanation":"Equality requires both differences to be empty; equal cardinalities alone are insufficient. The exact result, retaining the requested order, is (No, [-24], [25])."},"skills":["Set Equality with Both Difference Witnesses"],"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-20261008-advance-20261011-r04-set-0051","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae9f59d4887858a0304d91c879387dbc75526f2e006913bc32afcf2fd4fbb7c6","family_id":"qf-density11-set-candidate-partition","seed":202610114051,"semantic_template":"qf-density11-set-candidate-partition/[[],[]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[]; raw candidates=[] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([], [])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([], [])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0052","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61b38c01f22a2b93b7f286e272f37ad73796f214ebcf0e6dab1c2d3252a1d964","family_id":"qf-density11-set-candidate-partition","seed":202610114052,"semantic_template":"qf-density11-set-candidate-partition/[[0],[1]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[0]; raw candidates=[0, 1, 1] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([0], [1])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([0], [1])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0053","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9b4769704e173a73a53e1df9fab8cd79cb2defd9533510f3deaa6d89b29b351","family_id":"qf-density11-set-candidate-partition","seed":202610114053,"semantic_template":"qf-density11-set-candidate-partition/[[-2,0],[2]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-2, 0]; raw candidates=[-2, 2, 0, 2] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-2, 0], [2])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-2, 0], [2])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0054","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96ba77d5b0e4ea9359bcaa463db7b70838ebb4971e443d955e3573aa03fd70f9","family_id":"qf-density11-set-candidate-partition","seed":202610114054,"semantic_template":"qf-density11-set-candidate-partition/[[-3,0],[3]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-3, 0]; raw candidates=[-3, 3, 0, 3] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-3, 0], [3])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-3, 0], [3])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0055","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"204345bc379c77aa8db48d61aa8447758adc3225eaf268fdeefe6d6c65fe6113","family_id":"qf-density11-set-candidate-partition","seed":202610114055,"semantic_template":"qf-density11-set-candidate-partition/[[-4,0],[4]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-4, 0]; raw candidates=[-4, 4, 0, 4] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-4, 0], [4])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-4, 0], [4])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0056","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6cf8bc4b8b5fc620030eedd9daf61f315155bbae55f4a75b2f53292b3de1ce0","family_id":"qf-density11-set-candidate-partition","seed":202610114056,"semantic_template":"qf-density11-set-candidate-partition/[[-5,0],[5]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-5, 0]; raw candidates=[-5, 5, 0, 5] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-5, 0], [5])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-5, 0], [5])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0057","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8188366e3c78f3752846cd26bc3b9501d9ad61039cf5d2d094cb135aae4c6ecb","family_id":"qf-density11-set-candidate-partition","seed":202610114057,"semantic_template":"qf-density11-set-candidate-partition/[[-6,0],[6]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-6, 0]; raw candidates=[-6, 6, 0, 6] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-6, 0], [6])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-6, 0], [6])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0058","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"90156788176b50ab2a78471913fd1d787be23e2e8fff14d6f59db6fb9bfd5fc7","family_id":"qf-density11-set-candidate-partition","seed":202610114058,"semantic_template":"qf-density11-set-candidate-partition/[[-7,0],[7]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-7, 0]; raw candidates=[-7, 7, 0, 7] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-7, 0], [7])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-7, 0], [7])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0059","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"313f9d40799f4ffbe2229cdd00fa441494bc8fd44d2873fa970008d0ae5a2fd5","family_id":"qf-density11-set-candidate-partition","seed":202610114059,"semantic_template":"qf-density11-set-candidate-partition/[[-8,0],[8]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-8, 0]; raw candidates=[-8, 8, 0, 8] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-8, 0], [8])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-8, 0], [8])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0060","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2ca0e08646430b4ef00b966126a0cd36c5f2791a07d595418e164ba95bda4b21","family_id":"qf-density11-set-candidate-partition","seed":202610114060,"semantic_template":"qf-density11-set-candidate-partition/[[-9,0],[9]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-9, 0]; raw candidates=[-9, 9, 0, 9] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-9, 0], [9])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-9, 0], [9])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0061","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"09e101485003b021e32b97ee610a03a45dd7bf1e6c99d692c9354b21fd60e34a","family_id":"qf-density11-set-candidate-partition","seed":202610114061,"semantic_template":"qf-density11-set-candidate-partition/[[-10,0],[10]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-10, 0]; raw candidates=[-10, 10, 0, 10] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-10, 0], [10])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-10, 0], [10])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0062","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2b4ea78c53666581b9908aa689a18f94468b51f56516224309cf5e4532b1428a","family_id":"qf-density11-set-candidate-partition","seed":202610114062,"semantic_template":"qf-density11-set-candidate-partition/[[-11,0],[11]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-11, 0]; raw candidates=[-11, 11, 0, 11] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-11, 0], [11])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-11, 0], [11])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0063","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b7e0625e0982b548481e54acd660cc0868c734a0414cc30833bdc085c301afb","family_id":"qf-density11-set-candidate-partition","seed":202610114063,"semantic_template":"qf-density11-set-candidate-partition/[[-12,0],[12]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-12, 0]; raw candidates=[-12, 12, 0, 12] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-12, 0], [12])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-12, 0], [12])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0064","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee8f9acdb09c559e8a689b2f5e17561379b3ed8b0a25bfd2ce4c7d1aa25ddaee","family_id":"qf-density11-set-candidate-partition","seed":202610114064,"semantic_template":"qf-density11-set-candidate-partition/[[-13,0],[13]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-13, 0]; raw candidates=[-13, 13, 0, 13] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-13, 0], [13])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-13, 0], [13])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0065","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3226d855dc2bc0e7901cd709968b3a2c51e02579deb7969c3361a114e190b59e","family_id":"qf-density11-set-candidate-partition","seed":202610114065,"semantic_template":"qf-density11-set-candidate-partition/[[-14,0],[14]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-14, 0]; raw candidates=[-14, 14, 0, 14] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-14, 0], [14])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-14, 0], [14])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0066","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0a7258fc177ea1cd091fb6e40d78ac003147fb7a198d81ca11b487b3f1716e9a","family_id":"qf-density11-set-candidate-partition","seed":202610114066,"semantic_template":"qf-density11-set-candidate-partition/[[-15,0],[15]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-15, 0]; raw candidates=[-15, 15, 0, 15] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-15, 0], [15])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-15, 0], [15])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0067","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0a9d054d500f91fa39ff5b195d9dd7062c2eb2ddd52211217363cfd673423a53","family_id":"qf-density11-set-candidate-partition","seed":202610114067,"semantic_template":"qf-density11-set-candidate-partition/[[-16,0],[16]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-16, 0]; raw candidates=[-16, 16, 0, 16] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-16, 0], [16])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-16, 0], [16])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0068","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"71c48bce78e8803fd47754e7eadc19013a790c0108a9e50f61ab1ebd7de90e23","family_id":"qf-density11-set-candidate-partition","seed":202610114068,"semantic_template":"qf-density11-set-candidate-partition/[[-17,0],[17]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-17, 0]; raw candidates=[-17, 17, 0, 17] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-17, 0], [17])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-17, 0], [17])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0069","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f82db703c0238bc9d7ad2a00fa998a456022b09183aabf780cd60f4e37fda10","family_id":"qf-density11-set-candidate-partition","seed":202610114069,"semantic_template":"qf-density11-set-candidate-partition/[[-18,0],[18]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-18, 0]; raw candidates=[-18, 18, 0, 18] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-18, 0], [18])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-18, 0], [18])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0070","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2318b3df8ad08c0991cef9629800acb814088f122a6a5aacbb9a75f7f2d73032","family_id":"qf-density11-set-candidate-partition","seed":202610114070,"semantic_template":"qf-density11-set-candidate-partition/[[-19,0],[19]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-19, 0]; raw candidates=[-19, 19, 0, 19] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-19, 0], [19])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-19, 0], [19])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0071","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a77d40aea92db649e48a08d52a76575ee17f401cbfde22b3900baca5b8f19d8d","family_id":"qf-density11-set-candidate-partition","seed":202610114071,"semantic_template":"qf-density11-set-candidate-partition/[[-20,0],[20]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-20, 0]; raw candidates=[-20, 20, 0, 20] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-20, 0], [20])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-20, 0], [20])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0072","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ca68e738bce456c2b09903e7889b34130ee1c2c5789c822020728ba24aa38df","family_id":"qf-density11-set-candidate-partition","seed":202610114072,"semantic_template":"qf-density11-set-candidate-partition/[[-21,0],[21]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-21, 0]; raw candidates=[-21, 21, 0, 21] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-21, 0], [21])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-21, 0], [21])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0073","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ebb11176efd463b7bab42943ec7e9eeeb729068af0f8315a321cb450fb0651cf","family_id":"qf-density11-set-candidate-partition","seed":202610114073,"semantic_template":"qf-density11-set-candidate-partition/[[-22,0],[22]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-22, 0]; raw candidates=[-22, 22, 0, 22] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-22, 0], [22])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-22, 0], [22])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0074","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2cbb85f42f88d2dda66ca2dd2cebee9514fb61e0753e7ab77d6c14f505b17cab","family_id":"qf-density11-set-candidate-partition","seed":202610114074,"semantic_template":"qf-density11-set-candidate-partition/[[-23,0],[23]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-23, 0]; raw candidates=[-23, 23, 0, 23] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-23, 0], [23])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-23, 0], [23])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0075","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e737664dbdfab1db3ede667d9b0dc6e0aad9821fa06991dba6262f5123a39842","family_id":"qf-density11-set-candidate-partition","seed":202610114075,"semantic_template":"qf-density11-set-candidate-partition/[[-24,0],[24]]"},"fields":{"title":"Partition of an Explicit Candidate Set","stem":"Finite integer set A=[-24, 0]; raw candidates=[-24, 24, 0, 24] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.","answer":{"kind":"expression","value":"([-24, 0], [24])","explanation":"Normalize candidate repetition before membership tests; unlisted extra elements of A do not enter either output part. The exact result, retaining the requested order, is ([-24, 0], [24])."},"skills":["Partition of an Explicit Candidate Set"],"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-20261008-advance-20261011-r04-set-0076","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5725a9b00cc1754df302467729acff338b533c92294f9b5998117c2f4230fe1e","family_id":"qf-density11-set-powerset-enumeration","seed":202610114076,"semantic_template":"qf-density11-set-powerset-enumeration/[]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0077","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"05543fdbc84847fd4e3e2349d76b949bd94339d7b0998732634f53248485fbf9","family_id":"qf-density11-set-powerset-enumeration","seed":202610114077,"semantic_template":"qf-density11-set-powerset-enumeration/[0]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[0]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [0]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [0]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0078","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0898f1cc1178511c01cf4bc3c794a921a91132a863bbbf2f2fa1e289681dbfb1","family_id":"qf-density11-set-powerset-enumeration","seed":202610114078,"semantic_template":"qf-density11-set-powerset-enumeration/[-2,1]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-2, 1]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-2], [1], [-2, 1]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-2], [1], [-2, 1]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0079","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"07f930109c188343e81e126524743e53336aeb80e7500ba7070bc9efe04d912e","family_id":"qf-density11-set-powerset-enumeration","seed":202610114079,"semantic_template":"qf-density11-set-powerset-enumeration/[-3,0,1,3]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-3, 0, 1, 3]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-3], [0], [1], [3], [-3, 0], [-3, 1], [-3, 3], [0, 1], [0, 3], [1, 3], [-3, 0, 1], [-3, 0, 3], [-3, 1, 3], [0, 1, 3], [-3, 0, 1, 3]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-3], [0], [1], [3], [-3, 0], [-3, 1], [-3, 3], [0, 1], [0, 3], [1, 3], [-3, 0, 1], [-3, 0, 3], [-3, 1, 3], [0, 1, 3], [-3, 0, 1, 3]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0080","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"10f98f72defe3b7fedee0e0ef27813adbc92e15a796fcf8e418d657228992ccc","family_id":"qf-density11-set-powerset-enumeration","seed":202610114080,"semantic_template":"qf-density11-set-powerset-enumeration/[-4,0,1,4]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-4, 0, 1, 4]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-4], [0], [1], [4], [-4, 0], [-4, 1], [-4, 4], [0, 1], [0, 4], [1, 4], [-4, 0, 1], [-4, 0, 4], [-4, 1, 4], [0, 1, 4], [-4, 0, 1, 4]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-4], [0], [1], [4], [-4, 0], [-4, 1], [-4, 4], [0, 1], [0, 4], [1, 4], [-4, 0, 1], [-4, 0, 4], [-4, 1, 4], [0, 1, 4], [-4, 0, 1, 4]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0081","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5eb55a8e6edfbacd79e0ad04b6f1b00af2b330fd2493bd50252437c3b6c08306","family_id":"qf-density11-set-powerset-enumeration","seed":202610114081,"semantic_template":"qf-density11-set-powerset-enumeration/[-5,0,1,5]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-5, 0, 1, 5]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-5], [0], [1], [5], [-5, 0], [-5, 1], [-5, 5], [0, 1], [0, 5], [1, 5], [-5, 0, 1], [-5, 0, 5], [-5, 1, 5], [0, 1, 5], [-5, 0, 1, 5]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-5], [0], [1], [5], [-5, 0], [-5, 1], [-5, 5], [0, 1], [0, 5], [1, 5], [-5, 0, 1], [-5, 0, 5], [-5, 1, 5], [0, 1, 5], [-5, 0, 1, 5]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0082","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d95b330ad2b86c6b914f80b6c82de3fc843d55b2a73d1d42b907276b6f322a36","family_id":"qf-density11-set-powerset-enumeration","seed":202610114082,"semantic_template":"qf-density11-set-powerset-enumeration/[-6,0,1,6]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-6, 0, 1, 6]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-6], [0], [1], [6], [-6, 0], [-6, 1], [-6, 6], [0, 1], [0, 6], [1, 6], [-6, 0, 1], [-6, 0, 6], [-6, 1, 6], [0, 1, 6], [-6, 0, 1, 6]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-6], [0], [1], [6], [-6, 0], [-6, 1], [-6, 6], [0, 1], [0, 6], [1, 6], [-6, 0, 1], [-6, 0, 6], [-6, 1, 6], [0, 1, 6], [-6, 0, 1, 6]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0083","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"662a652d4165744a6c04d0d8487f6daaae1a3964444a0ca50f59ca38b2a1b348","family_id":"qf-density11-set-powerset-enumeration","seed":202610114083,"semantic_template":"qf-density11-set-powerset-enumeration/[-7,0,1,7]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-7, 0, 1, 7]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-7], [0], [1], [7], [-7, 0], [-7, 1], [-7, 7], [0, 1], [0, 7], [1, 7], [-7, 0, 1], [-7, 0, 7], [-7, 1, 7], [0, 1, 7], [-7, 0, 1, 7]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-7], [0], [1], [7], [-7, 0], [-7, 1], [-7, 7], [0, 1], [0, 7], [1, 7], [-7, 0, 1], [-7, 0, 7], [-7, 1, 7], [0, 1, 7], [-7, 0, 1, 7]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0084","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"154b7d9c38846d322c1ac0834d05bff503a54436a6ccfe857e82e68df199cfcd","family_id":"qf-density11-set-powerset-enumeration","seed":202610114084,"semantic_template":"qf-density11-set-powerset-enumeration/[-8,0,1,8]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-8, 0, 1, 8]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-8], [0], [1], [8], [-8, 0], [-8, 1], [-8, 8], [0, 1], [0, 8], [1, 8], [-8, 0, 1], [-8, 0, 8], [-8, 1, 8], [0, 1, 8], [-8, 0, 1, 8]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-8], [0], [1], [8], [-8, 0], [-8, 1], [-8, 8], [0, 1], [0, 8], [1, 8], [-8, 0, 1], [-8, 0, 8], [-8, 1, 8], [0, 1, 8], [-8, 0, 1, 8]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0085","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45b94a66eda282054c4b41fd8a39c4e5ed9f9ae3c4b825ef0f7bd226130dcd46","family_id":"qf-density11-set-powerset-enumeration","seed":202610114085,"semantic_template":"qf-density11-set-powerset-enumeration/[-9,0,1,9]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-9, 0, 1, 9]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-9], [0], [1], [9], [-9, 0], [-9, 1], [-9, 9], [0, 1], [0, 9], [1, 9], [-9, 0, 1], [-9, 0, 9], [-9, 1, 9], [0, 1, 9], [-9, 0, 1, 9]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-9], [0], [1], [9], [-9, 0], [-9, 1], [-9, 9], [0, 1], [0, 9], [1, 9], [-9, 0, 1], [-9, 0, 9], [-9, 1, 9], [0, 1, 9], [-9, 0, 1, 9]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0086","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"43b9110cfcca7bc9891975b6bdff267d05ee1f4a68fc5740c391756332ee20d4","family_id":"qf-density11-set-powerset-enumeration","seed":202610114086,"semantic_template":"qf-density11-set-powerset-enumeration/[-10,0,1,10]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-10, 0, 1, 10]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-10], [0], [1], [10], [-10, 0], [-10, 1], [-10, 10], [0, 1], [0, 10], [1, 10], [-10, 0, 1], [-10, 0, 10], [-10, 1, 10], [0, 1, 10], [-10, 0, 1, 10]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-10], [0], [1], [10], [-10, 0], [-10, 1], [-10, 10], [0, 1], [0, 10], [1, 10], [-10, 0, 1], [-10, 0, 10], [-10, 1, 10], [0, 1, 10], [-10, 0, 1, 10]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0087","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"24c2564fc768dd257cd6d8d75ccfa550ee44c4c712c50d04432f816e68b5726a","family_id":"qf-density11-set-powerset-enumeration","seed":202610114087,"semantic_template":"qf-density11-set-powerset-enumeration/[-11,0,1,11]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-11, 0, 1, 11]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-11], [0], [1], [11], [-11, 0], [-11, 1], [-11, 11], [0, 1], [0, 11], [1, 11], [-11, 0, 1], [-11, 0, 11], [-11, 1, 11], [0, 1, 11], [-11, 0, 1, 11]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-11], [0], [1], [11], [-11, 0], [-11, 1], [-11, 11], [0, 1], [0, 11], [1, 11], [-11, 0, 1], [-11, 0, 11], [-11, 1, 11], [0, 1, 11], [-11, 0, 1, 11]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0088","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3218af64340500c6715b749d1d0fd1ff73d3e11b0d8c9b1f2af85f96c6883802","family_id":"qf-density11-set-powerset-enumeration","seed":202610114088,"semantic_template":"qf-density11-set-powerset-enumeration/[-12,0,1,12]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-12, 0, 1, 12]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-12], [0], [1], [12], [-12, 0], [-12, 1], [-12, 12], [0, 1], [0, 12], [1, 12], [-12, 0, 1], [-12, 0, 12], [-12, 1, 12], [0, 1, 12], [-12, 0, 1, 12]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-12], [0], [1], [12], [-12, 0], [-12, 1], [-12, 12], [0, 1], [0, 12], [1, 12], [-12, 0, 1], [-12, 0, 12], [-12, 1, 12], [0, 1, 12], [-12, 0, 1, 12]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0089","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6046aa53d4a998a972a7e41abe0a19f3a28f89d744edb3bf87ae4a3082593384","family_id":"qf-density11-set-powerset-enumeration","seed":202610114089,"semantic_template":"qf-density11-set-powerset-enumeration/[-13,0,1,13]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-13, 0, 1, 13]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-13], [0], [1], [13], [-13, 0], [-13, 1], [-13, 13], [0, 1], [0, 13], [1, 13], [-13, 0, 1], [-13, 0, 13], [-13, 1, 13], [0, 1, 13], [-13, 0, 1, 13]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-13], [0], [1], [13], [-13, 0], [-13, 1], [-13, 13], [0, 1], [0, 13], [1, 13], [-13, 0, 1], [-13, 0, 13], [-13, 1, 13], [0, 1, 13], [-13, 0, 1, 13]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0090","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a7c6a70e581605479f57bef55075e40b14d1a5c82115ab6f57b7cf47fc70c920","family_id":"qf-density11-set-powerset-enumeration","seed":202610114090,"semantic_template":"qf-density11-set-powerset-enumeration/[-14,0,1,14]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-14, 0, 1, 14]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-14], [0], [1], [14], [-14, 0], [-14, 1], [-14, 14], [0, 1], [0, 14], [1, 14], [-14, 0, 1], [-14, 0, 14], [-14, 1, 14], [0, 1, 14], [-14, 0, 1, 14]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-14], [0], [1], [14], [-14, 0], [-14, 1], [-14, 14], [0, 1], [0, 14], [1, 14], [-14, 0, 1], [-14, 0, 14], [-14, 1, 14], [0, 1, 14], [-14, 0, 1, 14]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0091","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75127d1e1c830f5d16b33596c191195aa5c1524d56ece9b1def73f445a5c76ac","family_id":"qf-density11-set-powerset-enumeration","seed":202610114091,"semantic_template":"qf-density11-set-powerset-enumeration/[-15,0,1,15]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-15, 0, 1, 15]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-15], [0], [1], [15], [-15, 0], [-15, 1], [-15, 15], [0, 1], [0, 15], [1, 15], [-15, 0, 1], [-15, 0, 15], [-15, 1, 15], [0, 1, 15], [-15, 0, 1, 15]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-15], [0], [1], [15], [-15, 0], [-15, 1], [-15, 15], [0, 1], [0, 15], [1, 15], [-15, 0, 1], [-15, 0, 15], [-15, 1, 15], [0, 1, 15], [-15, 0, 1, 15]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0092","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3a94fd8834439db65ae80195e3ca4f86d1985c8a74454d93362927670c13de71","family_id":"qf-density11-set-powerset-enumeration","seed":202610114092,"semantic_template":"qf-density11-set-powerset-enumeration/[-16,0,1,16]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-16, 0, 1, 16]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-16], [0], [1], [16], [-16, 0], [-16, 1], [-16, 16], [0, 1], [0, 16], [1, 16], [-16, 0, 1], [-16, 0, 16], [-16, 1, 16], [0, 1, 16], [-16, 0, 1, 16]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-16], [0], [1], [16], [-16, 0], [-16, 1], [-16, 16], [0, 1], [0, 16], [1, 16], [-16, 0, 1], [-16, 0, 16], [-16, 1, 16], [0, 1, 16], [-16, 0, 1, 16]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0093","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a33f2e12265cb26dba9089deca8f14ce8815082ab9c8d6ff099768f7f8c61fea","family_id":"qf-density11-set-powerset-enumeration","seed":202610114093,"semantic_template":"qf-density11-set-powerset-enumeration/[-17,0,1,17]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-17, 0, 1, 17]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-17], [0], [1], [17], [-17, 0], [-17, 1], [-17, 17], [0, 1], [0, 17], [1, 17], [-17, 0, 1], [-17, 0, 17], [-17, 1, 17], [0, 1, 17], [-17, 0, 1, 17]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-17], [0], [1], [17], [-17, 0], [-17, 1], [-17, 17], [0, 1], [0, 17], [1, 17], [-17, 0, 1], [-17, 0, 17], [-17, 1, 17], [0, 1, 17], [-17, 0, 1, 17]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0094","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"72c31a74eac1a284f5b7a95254c668aeac3b34df8f809d1a03e4685d1270d58a","family_id":"qf-density11-set-powerset-enumeration","seed":202610114094,"semantic_template":"qf-density11-set-powerset-enumeration/[-18,0,1,18]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-18, 0, 1, 18]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-18], [0], [1], [18], [-18, 0], [-18, 1], [-18, 18], [0, 1], [0, 18], [1, 18], [-18, 0, 1], [-18, 0, 18], [-18, 1, 18], [0, 1, 18], [-18, 0, 1, 18]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-18], [0], [1], [18], [-18, 0], [-18, 1], [-18, 18], [0, 1], [0, 18], [1, 18], [-18, 0, 1], [-18, 0, 18], [-18, 1, 18], [0, 1, 18], [-18, 0, 1, 18]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0095","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f7c8ef6da384d6fdd40a31e820a62fc63a1f2d0000b5882d75160dddec201281","family_id":"qf-density11-set-powerset-enumeration","seed":202610114095,"semantic_template":"qf-density11-set-powerset-enumeration/[-19,0,1,19]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-19, 0, 1, 19]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-19], [0], [1], [19], [-19, 0], [-19, 1], [-19, 19], [0, 1], [0, 19], [1, 19], [-19, 0, 1], [-19, 0, 19], [-19, 1, 19], [0, 1, 19], [-19, 0, 1, 19]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-19], [0], [1], [19], [-19, 0], [-19, 1], [-19, 19], [0, 1], [0, 19], [1, 19], [-19, 0, 1], [-19, 0, 19], [-19, 1, 19], [0, 1, 19], [-19, 0, 1, 19]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0096","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"66d0dbfd4fe48ab3a3844417b754eed3905261a08abcd7737904dd742fbf365b","family_id":"qf-density11-set-powerset-enumeration","seed":202610114096,"semantic_template":"qf-density11-set-powerset-enumeration/[-20,0,1,20]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-20, 0, 1, 20]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-20], [0], [1], [20], [-20, 0], [-20, 1], [-20, 20], [0, 1], [0, 20], [1, 20], [-20, 0, 1], [-20, 0, 20], [-20, 1, 20], [0, 1, 20], [-20, 0, 1, 20]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-20], [0], [1], [20], [-20, 0], [-20, 1], [-20, 20], [0, 1], [0, 20], [1, 20], [-20, 0, 1], [-20, 0, 20], [-20, 1, 20], [0, 1, 20], [-20, 0, 1, 20]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0097","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9479685a16ca5f6050572c5005c125194af4e173cc8002c5ff6154a5a6ee759b","family_id":"qf-density11-set-powerset-enumeration","seed":202610114097,"semantic_template":"qf-density11-set-powerset-enumeration/[-21,0,1,21]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-21, 0, 1, 21]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-21], [0], [1], [21], [-21, 0], [-21, 1], [-21, 21], [0, 1], [0, 21], [1, 21], [-21, 0, 1], [-21, 0, 21], [-21, 1, 21], [0, 1, 21], [-21, 0, 1, 21]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-21], [0], [1], [21], [-21, 0], [-21, 1], [-21, 21], [0, 1], [0, 21], [1, 21], [-21, 0, 1], [-21, 0, 21], [-21, 1, 21], [0, 1, 21], [-21, 0, 1, 21]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0098","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b8b1dbc329a9f9d1a313b1a13a12359d18f4bb737a0be33b327f5432939eb2f4","family_id":"qf-density11-set-powerset-enumeration","seed":202610114098,"semantic_template":"qf-density11-set-powerset-enumeration/[-22,0,1,22]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-22, 0, 1, 22]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-22], [0], [1], [22], [-22, 0], [-22, 1], [-22, 22], [0, 1], [0, 22], [1, 22], [-22, 0, 1], [-22, 0, 22], [-22, 1, 22], [0, 1, 22], [-22, 0, 1, 22]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-22], [0], [1], [22], [-22, 0], [-22, 1], [-22, 22], [0, 1], [0, 22], [1, 22], [-22, 0, 1], [-22, 0, 22], [-22, 1, 22], [0, 1, 22], [-22, 0, 1, 22]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0099","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"67ecc59a3e285e5687dddb40f575e55847354db9a0966ecd3a6df34b7a43c9fc","family_id":"qf-density11-set-powerset-enumeration","seed":202610114099,"semantic_template":"qf-density11-set-powerset-enumeration/[-23,0,1,23]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-23, 0, 1, 23]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-23], [0], [1], [23], [-23, 0], [-23, 1], [-23, 23], [0, 1], [0, 23], [1, 23], [-23, 0, 1], [-23, 0, 23], [-23, 1, 23], [0, 1, 23], [-23, 0, 1, 23]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-23], [0], [1], [23], [-23, 0], [-23, 1], [-23, 23], [0, 1], [0, 23], [1, 23], [-23, 0, 1], [-23, 0, 23], [-23, 1, 23], [0, 1, 23], [-23, 0, 1, 23]]."},"skills":["Complete Finite Powerset"],"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-20261008-advance-20261011-r04-set-0100","batch_id":"batch-20261008-advance-20261011-r04-set-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"10d6b9021fa3b6eacc089c212ae31b295b27252b19a4f4e7de2953dbd4f8add5","family_id":"qf-density11-set-powerset-enumeration","seed":202610114100,"semantic_template":"qf-density11-set-powerset-enumeration/[-24,0,1,24]"},"fields":{"title":"Complete Finite Powerset","stem":"Finite integer set A=[-24, 0, 1, 24]. List all subsets, each increasingly ordered; order the outer list by size and then numeric lexicographic order. The empty set’s powerset contains the empty subset.","answer":{"kind":"expression","value":"[[], [-24], [0], [1], [24], [-24, 0], [-24, 1], [-24, 24], [0, 1], [0, 24], [1, 24], [-24, 0, 1], [-24, 0, 24], [-24, 1, 24], [0, 1, 24], [-24, 0, 1, 24]]","explanation":"Branch on including or excluding each distinct element, then apply the declared order; this finite construction is not unrestricted comprehension. The exact result, retaining the requested order, is [[], [-24], [0], [1], [24], [-24, 0], [-24, 1], [-24, 24], [0, 1], [0, 24], [1, 24], [-24, 0, 1], [-24, 0, 24], [-24, 1, 24], [0, 1, 24], [-24, 0, 1, 24]]."},"skills":["Complete Finite Powerset"],"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."}}