Prove that the relation of congruence is an equivalence relation.

illusiia 2020-11-08 Answered
Prove that the relation of congruence is an equivalence relation.
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ensojadasH
Answered 2020-11-09 Author has 100 answers
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 ab is denoted as a is congruent to b.
Step 2
Now,
Reflexive:
Since a aa, the relation is reflexive.
Symmetry:
Since ab then b a,the relation  is symmetry.
Transitivity:
Since ab and bc then ac , the relation is transitive.
Hence, the relation of congruence is an equivalence relation.
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