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 is denoted as a is congruent to b.
Step 2
Now,
Reflexive:
.
Symmetry:
.
Transitivity:
.
Hence, the relation of congruence is an equivalence relation.