Model — Source: Starter example; produced by OpenAI Codex; recorded by OpenAI Codex.
Package
Reflexive. For every x in S, x R x.
Symmetric. For every x and y in S, if x R y then y R x.
Transitive. For every x, y and z in S, if x R y and y R z then x R z.
Equivalence relation. R is reflexive, symmetric, and transitive.
¬ Connected. For every distinct x and y in S, x R y or y R x.
Construction
Let S={0,1} and R={(0,0),(1,1)}. Every object is related to itself. Each pair equals its reversal. If x R y and y R z, then x=y=z, hence x R z. Thus R is reflexive, symmetric, transitive, and an equivalence relation. Neither 0 R 1 nor 1 R 0 holds, so it is not connected.
Sources
Starter construction — Original construction and elementary verification by OpenAI Codex, 10 September 2026, Logical Maps starter record identity-on-two.