Let `m` be a given fixed positive integer. Let `R={(a.b) : a,b in Z` and `(a-b)` is divisible by `m}`. Show that `R` is an equivalence relation on `Z`.

Let n be a fixed positive integer. Define a relation R on Z as follows: (a , b)R a-b is divisible by ndot Show that R is an equivalence relation on Zdot

Let n be a fixed positive integer. Define a relation R on Z as follows: (a ,\ b) in RhArra-b is divisible by ndot Show that R is an equivalence relation on Zdot

Let n be a fixed positive integer. Define a relation R on Z as follows: (a ,\ b) in RhArra-b is divisible by ndot Show that R is an equivalence relation on Zdot

Let Z be the set of all integers and R be the relation on Z defined by R= { (a,b): a, b in Z and (a-b) is divisible by 5} . Prove that R is an equivalence relation

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.

Let Z be the set of all integers and R be the relation on Z defined as R={(a, b); a,\ b\ in Z, and (a-b) is divisible by 5} . Prove that R is an equivalence relation.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

Let Z be the set of integers. Show that the relation R={(a ,\ b): a ,\ b in Z and a+b is even} is an equivalence relation on Zdot

Let A = {1, 2, 3} and R = {(a,b): a,b in A, a divides b and b divides a}. Show that R is an identity relation on A.

Let R be a relation on the set A of ordered pairs of positive integers defined by (x , y) R (u , v) if and only if x v = y u . Show that R is an equivalence relation.