Let `R={(a,b):a,b inZ" and "(a-b)" is even"}.`
Then, show that R is an equivalence relation on Z.

Let R={(a,b):a,b in Z and (a-b) is divisible by 5}. Show that R is an equivalence relation on Z.

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 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 .

A relation R is defined on the set of integers Z Z as follows R= {(x,y) :x,y inZ Z and (x-y) is even } show that R is an equivalence relation on Z Z .

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 by R= { (a,b): a, b in Z and (a-b) is divisible by 5} . Prove that R is an equivalence relation

If Z is the set of all integers and R is the relation on Z defined as R={(a, b): a, b in Z and a-b is divisible by 3. 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 R be a relation on the set Q of all rationals defined by R={(a,b):a,binQ" and "a-binZ}. Show that R is an equivalence relation.