# Category:Equivalence Relations

This category contains results about Equivalence Relations.
Definitions specific to this category can be found in Definitions/Equivalence Relations.

Let $\mathcal R$ be a relation on a set $S$.

Let $\RR$ be:

$(1): \quad$ reflexive
$(2): \quad$ symmetric
$(3): \quad$ transitive

Then $\RR$ is an equivalence relation on $S$.