Equivalence relation ⇒ Symmetric

Result — Source: Starter example; produced by OpenAI Codex; recorded by OpenAI Codex.

Premises

• Equivalence relation. R is reflexive, symmetric, and transitive.

Conclusion

• Symmetric. For every x and y in S, if x R y then y R x.

Proof

By the definition of equivalence relation, R is reflexive, symmetric, and transitive. In particular it is symmetric. This holds for every nonempty set S and every relation R on S.

Sources

• Starter verification — Original elementary verification by OpenAI Codex, 10 September 2026, Logical Maps starter record equivalence-implies-symmetric.

Record: topics/example/results/equivalence-implies-symmetric.yaml