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Question 32043: Finite Set Intersection

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0063-32043 · q-20260915-finite-set-intersection-0018

Original question and givens

Let A={471, 472, 474} and B={473, 475, 476}. Find A∩B, listing each element once in increasing order.

  • G001 — Let A={471, 472, 474} and B={473, 475, 476}. Find A∩B, listing each element once in increasing order.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-finite-set-intersection, no-required-operation, no-required-domain, []]

After

derived = [[numeric_sorted_set_STRING_or_empty]]

Conditions: none

BASE sources do not acquire a generic legacy operation/domain or unknown-metadata ban.Retain metadata WITHOUT using it as an answer oracle.PULSE/legacy enforce their exact source keys,operation/domain.Do not impose universal tuples,/1 or input bounds.

Step identifiers and dependencies

Rule: R63_SOURCE_bank_keys_operation_domain_output_roles_metadata_not_oracle · Uses: G001

S002 · implies

Before

source roles = [A ORIGINAL, [471, 472, 474]]

After

derived = [[471, 472, 474]]

Conditions: none

THIS BASE set bank requires distinct integer lists;do not silently repair duplicates.Sort ONLY derived display,retaining originals.Do not import another bank SAFE/100-element bound.

Step identifiers and dependencies

Rule: Sets_BASE_distinct_integer_lists_no_SAFE_or100cap_no_silent_repair · Uses: G001, S001

S003 · implies

Before

source roles = [B ORIGINAL, [473, 475, 476]]

After

derived = [[473, 475, 476]]

Conditions: none

THIS BASE set bank requires distinct integer lists;do not silently repair duplicates.Sort ONLY derived display,retaining originals.Do not import another bank SAFE/100-element bound.

Step identifiers and dependencies

Rule: Sets_BASE_distinct_integer_lists_no_SAFE_or100cap_no_silent_repair · Uses: G001, S002

S004 · implies

Before

source roles = [qf-finite-set-intersection, 471, [471, 472, 474], [473, 475, 476]]

After

derived = [Yes, No, No]

Conditions: none

For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\B is not B\A;do not infer from order or pictures.

Step identifiers and dependencies

Rule: Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate · Uses: G001, S003

S005 · implies

Before

source roles = [qf-finite-set-intersection, 472, [471, 472, 474], [473, 475, 476]]

After

derived = [Yes, No, No]

Conditions: none

For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\B is not B\A;do not infer from order or pictures.

Step identifiers and dependencies

Rule: Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate · Uses: G001, S004

S006 · implies

Before

source roles = [qf-finite-set-intersection, 473, [471, 472, 474], [473, 475, 476]]

After

derived = [No, Yes, No]

Conditions: none

For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\B is not B\A;do not infer from order or pictures.

Step identifiers and dependencies

Rule: Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate · Uses: G001, S005

S007 · implies

Before

source roles = [qf-finite-set-intersection, 474, [471, 472, 474], [473, 475, 476]]

After

derived = [Yes, No, No]

Conditions: none

For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\B is not B\A;do not infer from order or pictures.

Step identifiers and dependencies

Rule: Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate · Uses: G001, S006

S008 · implies

Before

source roles = [qf-finite-set-intersection, 475, [471, 472, 474], [473, 475, 476]]

After

derived = [No, Yes, No]

Conditions: none

For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\B is not B\A;do not infer from order or pictures.

Step identifiers and dependencies

Rule: Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate · Uses: G001, S007

S009 · implies

Before

source roles = [qf-finite-set-intersection, 476, [471, 472, 474], [473, 475, 476]]

After

derived = [No, Yes, No]

Conditions: none

For EVERY label of A∪B check membership in A and B SEPARATELY,then apply THIS union/intersection/A-and-not-B predicate.A\B is not B\A;do not infer from order or pictures.

Step identifiers and dependencies

Rule: Sets_EVERY_union_label_TWO_memberships_AND_directional_predicate · Uses: G001, S008

S010 · implies

Before

source roles = [qf-finite-set-intersection, [471, 472, 474], [473, 475, 476]]

After

derived = [[], ∅, not-requested]

Conditions: none

AFTER every label,display the complete numeric increasing set once per element,or∅.For difference ALSO compute B\A to distinguish direction.Keep original A/B and source hashes.

Step identifiers and dependencies

Rule: Sets_COMPLETE_extensional_result_numeric_order_reverse_difference_separate · Uses: G001, S009

Reverse checks

  • S010 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S009 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S008 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S007 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S006 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S005 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S004 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S003 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S002 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
  • S001 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.

Result

∅

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 77ae6a2561233897b09ed4031d1bade655c20f20a2d39d31cd92f912839f9536
  • candidate record SHA-256: c81a50f93b2b3d9ef2ed8a910c400c61e658c0b812f3fbec3a275af6a916019b
  • semantic review receipt SHA-256: acf03b776f4855e3869810bcbecf1116e3a2b11dfb1e2a5dfbcf8135ad24a7d0
  • question-first witness SHA-256: eadbbac3220988b52754f32450fb536d627217306d1ce28a49134f56c21bfa88
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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