Definition:Trivial Equivalence Relation
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Definition
Let $S$ be a set.
Let $\RR$ be an equivalence relation on $S$.
Then $\RR$ is a trivial equivalence relation if and only if $\RR$ is either:
- the trivial relation $S \times S$
or:
- the diagonal relation $\Delta_S$ on $S$.
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 11$: Quotient Structures: Exercise $11.18$