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Question 4951: Outcome and Event Membership Masks

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0008-04951 · q-20261008-advance-20261011-r06-sample-space-0076

Original question and givens

Elementary outcomes are Fin(1)={0,…,0}, event E=[] is a subset of the space, and ordered candidates=[100, 101, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

  • G001 — Elementary outcomes are Fin(1)={0,…,0}, event E=[] is a subset of the space, and ordered candidates=[100, 101, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

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.

Step-by-step derivation

S001 · implies

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.

Step identifiers and dependencies

Rule: possible_outcomes_not_probabilities · Uses: G001

S002 · implies

Before

candidate=100;S=[0];E=[]

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.

Step identifiers and dependencies

Rule: possible_outcome_and_event_membership · Uses: G001, S001

S003 · implies

Before

candidate=101;S=[0];E=[]

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.

Step identifiers and dependencies

Rule: possible_outcome_and_event_membership · Uses: G001, S002

S004 · implies

Before

candidate=102;S=[0];E=[]

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.

Step identifiers and dependencies

Rule: possible_outcome_and_event_membership · Uses: G001, S003

Reverse checks

  • 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

([No, No, No], [No, No, 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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 389023cae4e229e4120033ca350fd1278f2743352f9ca59849ce1644f4498a54
  • candidate record SHA-256: 5be198a363ced6c5aaff22d0ba850aca654b31a5f10156b72617f499fc7cb685
  • semantic review receipt SHA-256: b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289
  • question-first witness SHA-256: caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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