Question 5010: Partition of an Explicit Candidate Set

Original question and givens

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.

• G001 — 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.

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-set

Step-by-step derivation

raw integer list=[-9, 0]

extensional set=[-9, 0]

candidate=-9;A=[-9, 0]

in A=Yes

candidate=0;A=[-9, 0]

in A=Yes

candidate=9;A=[-9, 0]

in A=No

[-9, 0, 9]

([-9, 0], [9])

Reverse checks

• 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.

Result

([-9, 0], [9])

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.