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R0009-05193 · q-20261008-advance-20261011-r05-subset-0043
Finite integer sets A=[-17, 0] and B=[0, 17]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.
G001 — Finite integer sets A=[-17, 0] and B=[0, 17]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.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.
Before
A=[-17, 0];B=[0, 17];same integer type
After
A⊆B means every A-element belongs to B
Conditions: none
An inclusion obstruction must belong to A but not B;an element outside A is no witness,and empty A gives no obstruction.
Rule: set_inclusion_definition · Uses: G001
Before
A\B:source element=-17;target=[0, 17]
After
obstruction=Yes
Conditions: none
Audit every source-set element;list it as an obstruction exactly when the target omits it.
Rule: inclusion_obstruction_row · Uses: G001, S001
Before
A\B:source element=0;target=[0, 17]
After
obstruction=No
Conditions: none
Audit every source-set element;list it as an obstruction exactly when the target omits it.
Rule: inclusion_obstruction_row · Uses: G001, S002
Before
B\A:source element=0;target=[-17, 0]
After
obstruction=No
Conditions: none
Audit every source-set element;list it as an obstruction exactly when the target omits it.
Rule: inclusion_obstruction_row · Uses: G001, S003
Before
B\A:source element=17;target=[-17, 0]
After
obstruction=Yes
Conditions: none
Audit every source-set element;list it as an obstruction exactly when the target omits it.
Rule: inclusion_obstruction_row · Uses: G001, S004
Before
A\B=[-17];B\A=[17]
After
non-strict=No;strict=No
Conditions: none
Strict inclusion requires A⊆B plus a B-element outside A;equal sets satisfy only non-strict inclusion.
Rule: strict_subset_extra_witness · Uses: G001, S005
S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.(No, No, [-17], [17])
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 714626c04614eef06b5e45fe887b0816b003aad446df83d678ef9ac48cf28775candidate record SHA-256: c384889aa7f8b5c19466d1e6ef0e369193db19810d7a54883c6ba073b9f47d12semantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462Lean: NOT_RUN · human review: NOT_PERFORMED