Relation R on Z, n a fixed integer.

a R b if and only if a-b is divisible by n a R a is true since a-a=0 is divisible by n

Hence R is reflexive

$ a R b =>b R a$

Since a R b if and only if (a-b) is divisible by n implies b R a if and only if (b-a) is divisible by n

(b-a)=-(a-b) since R is defined in Z

If a-b is divisible by n;-(a-b) is also divisible by n$

Hence R is symmetric

$a R b \in R;b R c \in R$

a-b is divisible by n. and b-c is divisible by n

But $(a-c)=(a-b)+(b-c)$

Hence a-c is also divisible by n

Solution:Therefore R is reflexive,symmetric and transitive

Hence R is an equivalnce relation