Question 8372: Relation Single-Valuedness versus Total-Function Qualification

Original question and givens

The explicitly typed relation R⊆Fin(3)×Fin(3) has ordered pairs=[[0, 0], [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, each source fiber size, at-most-one value per source?, exactly-one value per source?, total image table or not-a-total-function).

• G001 — The explicitly typed relation R⊆Fin(3)×Fin(3) has ordered pairs=[[0, 0], [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, each source fiber size, at-most-one value per source?, exactly-one value per source?, total image table or not-a-total-function).

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], [1, 1]]

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

source=0;pairs=[[0, 0], [1, 1]]

outgoing values=[0];count=1

source=1;pairs=[[0, 0], [1, 1]]

outgoing values=[1];count=1

source=2;pairs=[[0, 0], [1, 1]]

outgoing values=[];count=0

source fiber sizes=[1, 1, 0]

single-valued=Yes;exactly-one total=No;table/status=not a total function

Reverse checks

• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• 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

([3, 3], [[0, 0], [1, 1]], [1, 1, 0], Yes, No, not-a-total-function)

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.