# Prove that the relation of congruence is an equivalence relation.

Prove that the relation of congruence is an equivalence relation.
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Step 1
The definition of a congruence depends on the type of algebraic structure under consideration.
So, for the question “Prove that the relation of congruence is an equivalence relation.” we are taking in general.
Let $a\equiv b$ is denoted as a is congruent to b.
Step 2
Now,
Reflexive:
.
Symmetry:
.
Transitivity:
.
Hence, the relation of congruence is an equivalence relation.