Let S={33, 34, 35}, with F=P(S) explicitly selected. Is E={34, 41} an event in this model?
G001 — Let S={33, 34, 35}, with F=P(S) explicitly selected. Is E={34, 41} an event in this model?
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.
Check THIS bank interface:BASE equations use form/domain;BASE events/complement have no operation;factorials have no domain.ext18 uses local hyphens,other legacy operations underscores.Do not force every answer into a tuple or fraction.
The BASE finite set is a DISTINCT integer list;do not silently repair duplicates.Sort numerically ONLY for derived display,retaining original data.Do not import the expectation100-element or SAFE bounds.
source roles = [E original event candidate, [34, 41]]
After
derived = [[34, 41]]
Conditions: none
The BASE finite set is a DISTINCT integer list;do not silently repair duplicates.Sort numerically ONLY for derived display,retaining original data.Do not import the expectation100-element or SAFE bounds.
Check EACH candidate event element in ORIGINAL S.The empty event satisfies the subset condition vacuously.F=P(S)is not a probability law and does not imply equal likelihood.
Check EACH candidate event element in ORIGINAL S.The empty event satisfies the subset condition vacuously.F=P(S)is not a probability law and does not imply equal likelihood.
With EXACT F=P(S),event qualification is precisely E⊆S.An outside E is a LEGAL No in subset-validity;do not delete the witness first.Cardinality,occurrence and probability are distinct questions.
S006 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
S005 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
S004 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
S003 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
S002 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
S001 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,field roles,domain and premises.Consistency does not imply unique recovery of premises.Keep finite checking,independent review,formal proof and publication separate.
Result
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.