Question 8324: Typed Relation Projections and Missing Sources

Original question and givens

The explicitly typed relation R⊆Fin(3)×Fin(3) has ordered pairs=[[0, 0], [0, 1], [1, 1]]. Normalize repeated pairs as a set, in lexicographic order. A relation need not be single-valued or total; its converse need not be an inverse function. Give ([n,m], normalized pairs, source projection, target projection, pair count, missing source labels).

• G001 — The explicitly typed relation R⊆Fin(3)×Fin(3) has ordered pairs=[[0, 0], [0, 1], [1, 1]]. Normalize repeated pairs as a set, in lexicographic order. A relation need not be single-valued or total; its converse need not be an inverse function. Give ([n,m], normalized pairs, source projection, target projection, pair count, missing source labels).

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-relation

Step-by-step derivation

types=(3,3);raw ordered pairs=[[0, 0], [0, 1], [1, 1]]

normalized relation=[[0, 0], [0, 1], [1, 1]]

normalized pairs=[[0, 0], [0, 1], [1, 1]];declared sources=[0, 1, 2]

source projection=[0, 1];target projection=[0, 1];missing sources=[2];count=3

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

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

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.