Relation R = {(x,y) | x mod 3 = y mod 3}
For Example
4 mod 3 =1
7 mod 3 = 1
so (4,7) ∈ R
Reflexive : x mod 3 = x mod 3
Symmetric : If x mod 3 = y mod 3 then y mod 3 = x mod 3
Transitive : If x mod 3 = y mod 3, and y mod 3 = z mod 3, then x mod 3 = z mod 3
Therefore, the relation R is equivalence relation