This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.
This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20260915-finite-set-operations · 2026-09-15 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
Let A={1, 3, 5} and B={3, 4, 6}. Find A∪B, listing each element once in increasing order.
{1, 3, 4, 5, 6}
The union retains every element in A or B and lists duplicates only once, giving {1, 3, 4, 5, 6}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={11, 13, 15} and B={13, 14, 16}. Find A∪B, listing each element once in increasing order.
{11, 13, 14, 15, 16}
The union retains every element in A or B and lists duplicates only once, giving {11, 13, 14, 15, 16}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={21, 23, 25} and B={23, 24, 26}. Find A∪B, listing each element once in increasing order.
{21, 23, 24, 25, 26}
The union retains every element in A or B and lists duplicates only once, giving {21, 23, 24, 25, 26}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={31, 33, 35} and B={33, 34, 36}. Find A∪B, listing each element once in increasing order.
{31, 33, 34, 35, 36}
The union retains every element in A or B and lists duplicates only once, giving {31, 33, 34, 35, 36}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={41, 43, 45} and B={43, 44, 46}. Find A∪B, listing each element once in increasing order.
{41, 43, 44, 45, 46}
The union retains every element in A or B and lists duplicates only once, giving {41, 43, 44, 45, 46}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={51, 53, 55} and B={53, 54, 56}. Find A∪B, listing each element once in increasing order.
{51, 53, 54, 55, 56}
The union retains every element in A or B and lists duplicates only once, giving {51, 53, 54, 55, 56}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={61, 63, 65} and B={63, 64, 66}. Find A∪B, listing each element once in increasing order.
{61, 63, 64, 65, 66}
The union retains every element in A or B and lists duplicates only once, giving {61, 63, 64, 65, 66}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={71, 73, 75} and B={73, 74, 76}. Find A∪B, listing each element once in increasing order.
{71, 73, 74, 75, 76}
The union retains every element in A or B and lists duplicates only once, giving {71, 73, 74, 75, 76}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={81, 83, 85} and B={83, 84, 86}. Find A∪B, listing each element once in increasing order.
{81, 83, 84, 85, 86}
The union retains every element in A or B and lists duplicates only once, giving {81, 83, 84, 85, 86}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={91, 93, 95} and B={93, 94, 96}. Find A∪B, listing each element once in increasing order.
{91, 93, 94, 95, 96}
The union retains every element in A or B and lists duplicates only once, giving {91, 93, 94, 95, 96}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={101, 103, 105} and B={103, 104, 106}. Find A∪B, listing each element once in increasing order.
{101, 103, 104, 105, 106}
The union retains every element in A or B and lists duplicates only once, giving {101, 103, 104, 105, 106}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={111, 113, 115} and B={113, 114, 116}. Find A∪B, listing each element once in increasing order.
{111, 113, 114, 115, 116}
The union retains every element in A or B and lists duplicates only once, giving {111, 113, 114, 115, 116}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={121, 123, 125} and B={123, 124, 126}. Find A∪B, listing each element once in increasing order.
{121, 123, 124, 125, 126}
The union retains every element in A or B and lists duplicates only once, giving {121, 123, 124, 125, 126}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={131, 133, 135} and B={133, 134, 136}. Find A∪B, listing each element once in increasing order.
{131, 133, 134, 135, 136}
The union retains every element in A or B and lists duplicates only once, giving {131, 133, 134, 135, 136}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={141, 143, 145} and B={143, 144, 146}. Find A∪B, listing each element once in increasing order.
{141, 143, 144, 145, 146}
The union retains every element in A or B and lists duplicates only once, giving {141, 143, 144, 145, 146}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={151, 153, 155} and B={153, 154, 156}. Find A∪B, listing each element once in increasing order.
{151, 153, 154, 155, 156}
The union retains every element in A or B and lists duplicates only once, giving {151, 153, 154, 155, 156}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={161, 163, 165} and B={163, 164, 166}. Find A∪B, listing each element once in increasing order.
{161, 163, 164, 165, 166}
The union retains every element in A or B and lists duplicates only once, giving {161, 163, 164, 165, 166}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={171, 173, 175} and B={173, 174, 176}. Find A∪B, listing each element once in increasing order.
{171, 173, 174, 175, 176}
The union retains every element in A or B and lists duplicates only once, giving {171, 173, 174, 175, 176}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={181, 183, 185} and B={183, 184, 186}. Find A∪B, listing each element once in increasing order.
{181, 183, 184, 185, 186}
The union retains every element in A or B and lists duplicates only once, giving {181, 183, 184, 185, 186}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={191, 193, 195} and B={193, 194, 196}. Find A∪B, listing each element once in increasing order.
{191, 193, 194, 195, 196}
The union retains every element in A or B and lists duplicates only once, giving {191, 193, 194, 195, 196}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={201, 203, 205} and B={203, 204, 206}. Find A∪B, listing each element once in increasing order.
{201, 203, 204, 205, 206}
The union retains every element in A or B and lists duplicates only once, giving {201, 203, 204, 205, 206}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={211, 213, 215} and B={213, 214, 216}. Find A∪B, listing each element once in increasing order.
{211, 213, 214, 215, 216}
The union retains every element in A or B and lists duplicates only once, giving {211, 213, 214, 215, 216}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={221, 223, 225} and B={223, 224, 226}. Find A∪B, listing each element once in increasing order.
{221, 223, 224, 225, 226}
The union retains every element in A or B and lists duplicates only once, giving {221, 223, 224, 225, 226}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={231, 233, 235} and B={233, 234, 236}. Find A∪B, listing each element once in increasing order.
{231, 233, 234, 235, 236}
The union retains every element in A or B and lists duplicates only once, giving {231, 233, 234, 235, 236}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={241, 243, 245} and B={243, 244, 246}. Find A∪B, listing each element once in increasing order.
{241, 243, 244, 245, 246}
The union retains every element in A or B and lists duplicates only once, giving {241, 243, 244, 245, 246}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-union · candidate
Let A={301, 302, 304} and B={302, 304, 306}. Find A∩B, listing each element once in increasing order.
{302, 304}
The intersection retains exactly the elements common to A and B, giving {302, 304}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={311, 312, 314} and B={313, 315, 316}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={321, 322, 324} and B={322, 324, 326}. Find A∩B, listing each element once in increasing order.
{322, 324}
The intersection retains exactly the elements common to A and B, giving {322, 324}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={331, 332, 334} and B={333, 335, 336}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={341, 342, 344} and B={342, 344, 346}. Find A∩B, listing each element once in increasing order.
{342, 344}
The intersection retains exactly the elements common to A and B, giving {342, 344}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={351, 352, 354} and B={353, 355, 356}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={361, 362, 364} and B={362, 364, 366}. Find A∩B, listing each element once in increasing order.
{362, 364}
The intersection retains exactly the elements common to A and B, giving {362, 364}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={371, 372, 374} and B={373, 375, 376}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={381, 382, 384} and B={382, 384, 386}. Find A∩B, listing each element once in increasing order.
{382, 384}
The intersection retains exactly the elements common to A and B, giving {382, 384}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={391, 392, 394} and B={393, 395, 396}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={401, 402, 404} and B={402, 404, 406}. Find A∩B, listing each element once in increasing order.
{402, 404}
The intersection retains exactly the elements common to A and B, giving {402, 404}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={411, 412, 414} and B={413, 415, 416}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={421, 422, 424} and B={422, 424, 426}. Find A∩B, listing each element once in increasing order.
{422, 424}
The intersection retains exactly the elements common to A and B, giving {422, 424}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={431, 432, 434} and B={433, 435, 436}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={441, 442, 444} and B={442, 444, 446}. Find A∩B, listing each element once in increasing order.
{442, 444}
The intersection retains exactly the elements common to A and B, giving {442, 444}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={451, 452, 454} and B={453, 455, 456}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={461, 462, 464} and B={462, 464, 466}. Find A∩B, listing each element once in increasing order.
{462, 464}
The intersection retains exactly the elements common to A and B, giving {462, 464}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={471, 472, 474} and B={473, 475, 476}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={481, 482, 484} and B={482, 484, 486}. Find A∩B, listing each element once in increasing order.
{482, 484}
The intersection retains exactly the elements common to A and B, giving {482, 484}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={491, 492, 494} and B={493, 495, 496}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={501, 502, 504} and B={502, 504, 506}. Find A∩B, listing each element once in increasing order.
{502, 504}
The intersection retains exactly the elements common to A and B, giving {502, 504}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={511, 512, 514} and B={513, 515, 516}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={521, 522, 524} and B={522, 524, 526}. Find A∩B, listing each element once in increasing order.
{522, 524}
The intersection retains exactly the elements common to A and B, giving {522, 524}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={531, 532, 534} and B={533, 535, 536}. Find A∩B, listing each element once in increasing order.
∅
The intersection retains exactly the elements common to A and B, giving ∅.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={541, 542, 544} and B={542, 544, 546}. Find A∩B, listing each element once in increasing order.
{542, 544}
The intersection retains exactly the elements common to A and B, giving {542, 544}.
Reviewed step-by-step derivation
Set operations · qf-finite-set-intersection · candidate
Let A={601, 602, 604, 606} and B={602, 605, 606}. Find the directional difference A\B, listing each element once in increasing order.
{601, 604}
A\B retains elements in A that are not in B, giving {601, 604}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={611, 612, 614, 616} and B={612, 615, 616}. Find the directional difference A\B, listing each element once in increasing order.
{611, 614}
A\B retains elements in A that are not in B, giving {611, 614}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={621, 622, 624, 626} and B={622, 625, 626}. Find the directional difference A\B, listing each element once in increasing order.
{621, 624}
A\B retains elements in A that are not in B, giving {621, 624}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={631, 632, 634, 636} and B={632, 635, 636}. Find the directional difference A\B, listing each element once in increasing order.
{631, 634}
A\B retains elements in A that are not in B, giving {631, 634}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={641, 642, 644, 646} and B={642, 645, 646}. Find the directional difference A\B, listing each element once in increasing order.
{641, 644}
A\B retains elements in A that are not in B, giving {641, 644}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={651, 652, 654, 656} and B={652, 655, 656}. Find the directional difference A\B, listing each element once in increasing order.
{651, 654}
A\B retains elements in A that are not in B, giving {651, 654}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={661, 662, 664, 666} and B={662, 665, 666}. Find the directional difference A\B, listing each element once in increasing order.
{661, 664}
A\B retains elements in A that are not in B, giving {661, 664}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={671, 672, 674, 676} and B={672, 675, 676}. Find the directional difference A\B, listing each element once in increasing order.
{671, 674}
A\B retains elements in A that are not in B, giving {671, 674}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={681, 682, 684, 686} and B={682, 685, 686}. Find the directional difference A\B, listing each element once in increasing order.
{681, 684}
A\B retains elements in A that are not in B, giving {681, 684}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={691, 692, 694, 696} and B={692, 695, 696}. Find the directional difference A\B, listing each element once in increasing order.
{691, 694}
A\B retains elements in A that are not in B, giving {691, 694}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={701, 702, 704, 706} and B={702, 705, 706}. Find the directional difference A\B, listing each element once in increasing order.
{701, 704}
A\B retains elements in A that are not in B, giving {701, 704}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={711, 712, 714, 716} and B={712, 715, 716}. Find the directional difference A\B, listing each element once in increasing order.
{711, 714}
A\B retains elements in A that are not in B, giving {711, 714}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={721, 722, 724, 726} and B={722, 725, 726}. Find the directional difference A\B, listing each element once in increasing order.
{721, 724}
A\B retains elements in A that are not in B, giving {721, 724}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={731, 732, 734, 736} and B={732, 735, 736}. Find the directional difference A\B, listing each element once in increasing order.
{731, 734}
A\B retains elements in A that are not in B, giving {731, 734}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={741, 742, 744, 746} and B={742, 745, 746}. Find the directional difference A\B, listing each element once in increasing order.
{741, 744}
A\B retains elements in A that are not in B, giving {741, 744}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={751, 752, 754, 756} and B={752, 755, 756}. Find the directional difference A\B, listing each element once in increasing order.
{751, 754}
A\B retains elements in A that are not in B, giving {751, 754}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={761, 762, 764, 766} and B={762, 765, 766}. Find the directional difference A\B, listing each element once in increasing order.
{761, 764}
A\B retains elements in A that are not in B, giving {761, 764}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={771, 772, 774, 776} and B={772, 775, 776}. Find the directional difference A\B, listing each element once in increasing order.
{771, 774}
A\B retains elements in A that are not in B, giving {771, 774}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={781, 782, 784, 786} and B={782, 785, 786}. Find the directional difference A\B, listing each element once in increasing order.
{781, 784}
A\B retains elements in A that are not in B, giving {781, 784}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={791, 792, 794, 796} and B={792, 795, 796}. Find the directional difference A\B, listing each element once in increasing order.
{791, 794}
A\B retains elements in A that are not in B, giving {791, 794}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={801, 802, 804, 806} and B={802, 805, 806}. Find the directional difference A\B, listing each element once in increasing order.
{801, 804}
A\B retains elements in A that are not in B, giving {801, 804}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={811, 812, 814, 816} and B={812, 815, 816}. Find the directional difference A\B, listing each element once in increasing order.
{811, 814}
A\B retains elements in A that are not in B, giving {811, 814}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={821, 822, 824, 826} and B={822, 825, 826}. Find the directional difference A\B, listing each element once in increasing order.
{821, 824}
A\B retains elements in A that are not in B, giving {821, 824}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={831, 832, 834, 836} and B={832, 835, 836}. Find the directional difference A\B, listing each element once in increasing order.
{831, 834}
A\B retains elements in A that are not in B, giving {831, 834}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let A={841, 842, 844, 846} and B={842, 845, 846}. Find the directional difference A\B, listing each element once in increasing order.
{841, 844}
A\B retains elements in A that are not in B, giving {841, 844}. Reversing the operands is a different operation.
Reviewed step-by-step derivation
Set operations · qf-finite-set-difference · candidate
Let the explicit universe be U={901, 902, 903, 904, 905} and A={901, 903}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{902, 904, 905}
The universe is explicit and A⊆U. Removing A from U gives {902, 904, 905}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={911, 912, 913, 914, 915} and A={912, 914, 915}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{911, 913}
The universe is explicit and A⊆U. Removing A from U gives {911, 913}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={921, 922, 923, 924, 925} and A={921, 923}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{922, 924, 925}
The universe is explicit and A⊆U. Removing A from U gives {922, 924, 925}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={931, 932, 933, 934, 935} and A={932, 934, 935}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{931, 933}
The universe is explicit and A⊆U. Removing A from U gives {931, 933}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={941, 942, 943, 944, 945} and A={941, 943}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{942, 944, 945}
The universe is explicit and A⊆U. Removing A from U gives {942, 944, 945}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={951, 952, 953, 954, 955} and A={952, 954, 955}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{951, 953}
The universe is explicit and A⊆U. Removing A from U gives {951, 953}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={961, 962, 963, 964, 965} and A={961, 963}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{962, 964, 965}
The universe is explicit and A⊆U. Removing A from U gives {962, 964, 965}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={971, 972, 973, 974, 975} and A={972, 974, 975}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{971, 973}
The universe is explicit and A⊆U. Removing A from U gives {971, 973}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={981, 982, 983, 984, 985} and A={981, 983}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{982, 984, 985}
The universe is explicit and A⊆U. Removing A from U gives {982, 984, 985}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={991, 992, 993, 994, 995} and A={992, 994, 995}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{991, 993}
The universe is explicit and A⊆U. Removing A from U gives {991, 993}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1001, 1002, 1003, 1004, 1005} and A={1001, 1003}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1002, 1004, 1005}
The universe is explicit and A⊆U. Removing A from U gives {1002, 1004, 1005}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1011, 1012, 1013, 1014, 1015} and A={1012, 1014, 1015}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1011, 1013}
The universe is explicit and A⊆U. Removing A from U gives {1011, 1013}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1021, 1022, 1023, 1024, 1025} and A={1021, 1023}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1022, 1024, 1025}
The universe is explicit and A⊆U. Removing A from U gives {1022, 1024, 1025}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1031, 1032, 1033, 1034, 1035} and A={1032, 1034, 1035}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1031, 1033}
The universe is explicit and A⊆U. Removing A from U gives {1031, 1033}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1041, 1042, 1043, 1044, 1045} and A={1041, 1043}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1042, 1044, 1045}
The universe is explicit and A⊆U. Removing A from U gives {1042, 1044, 1045}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1051, 1052, 1053, 1054, 1055} and A={1052, 1054, 1055}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1051, 1053}
The universe is explicit and A⊆U. Removing A from U gives {1051, 1053}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1061, 1062, 1063, 1064, 1065} and A={1061, 1063}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1062, 1064, 1065}
The universe is explicit and A⊆U. Removing A from U gives {1062, 1064, 1065}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1071, 1072, 1073, 1074, 1075} and A={1072, 1074, 1075}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1071, 1073}
The universe is explicit and A⊆U. Removing A from U gives {1071, 1073}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1081, 1082, 1083, 1084, 1085} and A={1081, 1083}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1082, 1084, 1085}
The universe is explicit and A⊆U. Removing A from U gives {1082, 1084, 1085}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1091, 1092, 1093, 1094, 1095} and A={1092, 1094, 1095}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1091, 1093}
The universe is explicit and A⊆U. Removing A from U gives {1091, 1093}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1101, 1102, 1103, 1104, 1105} and A={1101, 1103}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1102, 1104, 1105}
The universe is explicit and A⊆U. Removing A from U gives {1102, 1104, 1105}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1111, 1112, 1113, 1114, 1115} and A={1112, 1114, 1115}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1111, 1113}
The universe is explicit and A⊆U. Removing A from U gives {1111, 1113}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1121, 1122, 1123, 1124, 1125} and A={1121, 1123}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1122, 1124, 1125}
The universe is explicit and A⊆U. Removing A from U gives {1122, 1124, 1125}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1131, 1132, 1133, 1134, 1135} and A={1132, 1134, 1135}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1131, 1133}
The universe is explicit and A⊆U. Removing A from U gives {1131, 1133}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Let the explicit universe be U={1141, 1142, 1143, 1144, 1145} and A={1141, 1143}⊆U. Find the relative complement U\A, listing each element once in increasing order.
{1142, 1144, 1145}
The universe is explicit and A⊆U. Removing A from U gives {1142, 1144, 1145}.
Reviewed step-by-step derivation
Set operations · qf-finite-relative-complement · candidate
Canonical question JSONL · English JSONL · Validation report