# Equivalence Relation

A relation defined on a set A is called equivalence relation, if it is reflexive, symmetric and transitive. In mathematics, we have many relations that are reflexive, symmetric and transitive. This is the most important relation in math.

A relation R is said to be an equivalence relation if it is reflexive, symmetric and transitive. So, we can say if,

- (a, b) $\in$ R, $\forall$ a, b ∈ A.
- (a, b) $\in$ R $\Rightarrow$ (b, a) $\in$ R, for all a, b ∈ A.
- (a, b) $\in$ R and (b, c) $\in$ R $\Rightarrow$ (a, c) $\in$ R, $\forall$ a, b, c $\in$ A.