Connected ∧ Symmetric ⇒ Transitive

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

Premises

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

Conclusion

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

Notes

Deliberately unresolved by the supplied records, not asserted to be an open research problem. Add a proof or a checked countermodel as an exercise.

Sources

• Starter exercise — Tutorial exercise recorded by OpenAI Codex, 10 September 2026, Logical Maps starter.

Record: topics/example/results/connected-symmetric-implies-transitive.yaml