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R0008-04957 · q-20261008-advance-20261011-r06-sample-space-0082
Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 2, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.
G001 — Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 2, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.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.
Before
explicit finite possible-outcome protocol
After
no probability law,equiprobability or independence inferred
Conditions: none
These tasks list possible outcomes,recordings or event membership without assigning probabilities.All combinations being possible does not imply equiprobability or independence.
Rule: possible_outcomes_not_probabilities · Uses: G001
Before
candidate=1;S=[0, 1, 2, 3, 4, 5];E=[1, 2, 3]
After
in S=Yes;in E=Yes
Conditions: none
Event E is a subset of S,not a single outcome.An outside candidate is not in E;retain the original candidate order.
Rule: possible_outcome_and_event_membership · Uses: G001, S001
Before
candidate=2;S=[0, 1, 2, 3, 4, 5];E=[1, 2, 3]
After
in S=Yes;in E=Yes
Conditions: none
Event E is a subset of S,not a single outcome.An outside candidate is not in E;retain the original candidate order.
Rule: possible_outcome_and_event_membership · Uses: G001, S002
Before
candidate=102;S=[0, 1, 2, 3, 4, 5];E=[1, 2, 3]
After
in S=No;in E=No
Conditions: none
Event E is a subset of S,not a single outcome.An outside candidate is not in E;retain the original candidate order.
Rule: possible_outcome_and_event_membership · Uses: G001, S003
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.([Yes, Yes, No], [Yes, Yes, No])
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 24436c0837f7b695d9d4396b84a86e69d9643c9a89ba55ec54d4d02901c24453candidate record SHA-256: f856e01c9e25cae0c470a94ef825d395ae1c82a8d8f85b4f9746830da2b21456semantic review receipt SHA-256: b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289question-first witness SHA-256: caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67Lean: NOT_RUN · human review: NOT_PERFORMED