[" I let "R" be u relation on "Z" defined by "],[R={(a,b):a-b" is even "}" prove that "R" is "],[" an equivalence relation."]

Let R be the relation on Z defined by aRb iff a-b is an even integer. Show 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 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.

In the set of all natural numbers,let a relation defined by {(a,b):a,binN,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 the relation on Z defined by R = {(a,b),a, b in Z,a^2 =b^2} Find R

Show that the relation R defined by R={(a,b):a-b is divisible by 3;a,b in Z} is an equivalence relation.