Let P be the set of all triangles in a plane and R be the relation defined on P as a Rb if a is similar to b. 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.

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

Let N be the set of all natural numbers and R be the relation in NxxN defined by (a,b) R (c,d), if ad=bc. Show 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 A be the set of all students of class XII in a school and R be the relation, having the same sex on A, and then prove that R is an equivalence relation.

Let Z be the set of a integers and let R be a relation on z defined by a Rb hArr a>=b. Then,R is