Question 5110: Candidate Inclusion-Counterexample Mask

Original question and givens

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 101, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

• G001 — Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 101, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

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.

• mko-subset

Step-by-step derivation

A=[-3, -2, -1, 1, 2, 3];B=[1, 2, 3];same integer type

A⊆B means every A-element belongs to B

candidate=-1;in A=Yes;in B=No

Yes

candidate=101;in A=No;in B=No

No

candidate=3;in A=Yes;in B=Yes

No

Reverse checks

• 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.

Result

[Yes, No, No]

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.