Question 34989: First Projection of a Binary Relation

Original question and givens

The binary relation has source A={1, 2, 3}, target B={5, 6, 7}, and R={(1, 5)}⊆A×B. List its actual domain Dom(R) in increasing order with each element once.

• G001 — The binary relation has source A={1, 2, 3}, target B={5, 6, 7}, and R={(1, 5)}⊆A×B. List its actual domain Dom(R) in increasing order with each element once.

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

source roles = [qf-relation-domain-projection, [A, B, R, operation]]

derived = [domain_projection, no-invented-domain]

source roles = [relation ORIGINAL source A, [1, 2, 3]]

derived = [[1, 2, 3]]

source roles = [relation ORIGINAL target B, [5, 6, 7]]

derived = [[5, 6, 7]]

source roles = [0, [1, 5]]

derived = [[1, 5]]

source roles = [[1, 2, 3], [5, 6, 7], [[1, 5]]]

derived = [Yes]

source roles = [[1, 2, 3], [5, 6, 7], [[1, 5]]]

derived = [[1], {1}]

Reverse checks

• S006 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.
• S005 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.
• S004 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.
• S003 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.
• S002 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.
• S001 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.

Result

{1}

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.