Question 6001: Event Union, Intersection, and Outside Complement

Original question and givens

S=Fin(1)={0,…,0}; the event family is explicitly F=P(S). A=[], B=[] are subsets of S. Give (A∪B, A∩B, S\(A∪B)), each deduplicated and increasing.

• G001 — S=Fin(1)={0,…,0}; the event family is explicitly F=P(S). A=[], B=[] are subsets of S. Give (A∪B, A∩B, S\(A∪B)), each deduplicated and increasing.

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(1)=[0];declared event model=full_powerset

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

outcome=0;in A=No;in B=No

in union=No;in intersection=No;outside union=Yes

Reverse checks

• 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])

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.