Definition:Trivial Equivalence Relation

Definition
Let $S$ be a set.

Let $\RR$ be an equivalence relation on $S$.

Then $\RR$ is a trivial equivalence relation $\RR$ is either:
 * the trivial relation $S \times S$

or:
 * the diagonal relation $\Delta_S$ on $S$.

Also see

 * Trivial Relation is Equivalence
 * Diagonal Relation is Equivalence