Question 4388: Complete Finite Predicate Partition

Original question and givens

The explicitly finite integer domain is U=[-12, -1, 0, 1, 12] and P(x) means x≥0. Give (elements satisfying P, elements not satisfying P), each sorted increasingly.

• G001 — The explicitly finite integer domain is U=[-12, -1, 0, 1, 12] and P(x) means x≥0. Give (elements satisfying P, elements not satisfying P), 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-quantifier

Step-by-step derivation

complete finite U=[-12, -1, 0, 1, 12]

universal on empty domain=True;existential on empty domain=False

x=-12;predicate=ge 0

P(x)=No

x=-1;predicate=ge 0

P(x)=No

x=0;predicate=ge 0

P(x)=Yes

x=1;predicate=ge 0

P(x)=Yes

x=12;predicate=ge 0

P(x)=Yes

[[-12, No], [-1, No], [0, Yes], [1, Yes], [12, Yes]]

T=[0, 1, 12];F=[-12, -1];T∪F=U and T∩F=∅

Reverse checks

• S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• 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.

Result

([0, 1, 12], [-12, -1])

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.