Connected Equivalence Relation is Trivial/Examples

Examples of Connected Equivalence Relation is Trivial

Arbitrary Set of 4 Elements

Let $V = \set {a, b, c, d}$.

Let $S \subseteq V \times V$ such that:

$S = \set {\tuple {a, b}, \tuple {b, c}, \tuple {c, d} }$

Let $\RR$ be an equivalence relation on $V$ such that:

$S \subseteq \RR$

Then $\RR$ is the trivial relation on $S$.