Question

What is Equivalence Relation?

Answer 1

Equivalence Relation : $~ A$ relation $R$ on a set $A$ is said to be an equivalence relation if

(i) R is reflexive i.e. $(x, x) \in R, \forall x \in A$

(ii) R is symmetric i.e. $(x, y) \in R \Rightarrow(y, x) \in R$ where $x, y \in A$.

(iii) R is transitive i.e. $(x, y) \in R$ and $(y, z) \in R \Rightarrow(x, z) \in R$, where $x, y, z \in A$.