Prove that the relation of congruence is an equivalence relation.

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:
$Sincea\equiv a\mathrm{\forall }a,therelation\equiv isreflexive$.
Symmetry:
$Sincea\equiv bthenb\equiv a,therelation\equiv issymmetry$.
Transitivity:
$Sincea\equiv bandb\equiv cthena\equiv c,therelation\equiv istransitive$.
Hence, the relation of congruence is an equivalence relation.