Question 6139: Ordered Opposites and Two Difference Directions

Original question and givens

Integers a=1, b=-12. Give (−a, −b, a−b, b−a), retaining signs and direction.

• G001 — Integers a=1, b=-12. Give (−a, −b, a−b, b−a), retaining signs and direction.

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-integer

Step-by-step derivation

declared exact integer or rational-representation protocol

retain signs,ordered operands and original index order

opposite of a := mul(-1, 1)

opposite of a = -1

opposite of b := mul(-1, -12)

opposite of b = 12

a minus b := sub(1, -12)

a minus b = 13

b minus a := sub(-12, 1)

b minus a = -13

Reverse checks

• S005 · premise_and_result_audit — Recompute b minus a with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute a minus b with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute opposite of b with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute opposite of a with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(-1, 12, 13, -13)

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.