One of the most important relation, which plays a significant role in Mathematics,
is an equivalence relation To study equivalence relation, we first consider three
types of relations, namely reflexive, symmetric and transitive Definition 3 A relation R in a set A is called
(i)
reflexive, if (a, a) ∈ R, for every a ∈ A,
(ii)
symmetric, if (a1, a2) ∈ R implies that (a2, a1) ∈ R, for all a1, a2 ∈ A (iii)
transitive, if (a1, a2) ∈ R and (a2, a3) ∈ R implies that (a1, a3) ∈ R, for all a1, a2,
a3 ∈ A