Question 6028: Declared Event and Relative Complement Partition

Original question and givens

S=Fin(5)={0,…,4}; the event family is explicitly F=P(S). E=[0]⊆S. Give (increasing E, increasing S\E, n).

• G001 — S=Fin(5)={0,…,4}; the event family is explicitly F=P(S). E=[0]⊆S. Give (increasing E, increasing S\E, n).

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-event

Step-by-step derivation

S=Fin(5)=[0, 1, 2, 3, 4];declared event model=full_powerset

finite S alone does not specify its event family or a probability law

E=[0];S=[0, 1, 2, 3, 4]

S\E=[1, 2, 3, 4]

([0], [1, 2, 3, 4])

disjoint union is S;|S|=5

Reverse checks

• 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, 2, 3, 4], 5)

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.