In the set Z of integers define `mRn` if `m-n ` is a multiple of `12`. Prove the `R` is an equivalence relation.

In the set Z of integers, define m Rn if m-n is a multiple of 12. Prove that R is an equivalence relation.

In the set Z of integers, define mRn if m-n is divisible by 7. Prove that R is an equivalence relation.

In the set of integers Z, define mRn if m-n is a multiple of 5. Is R equivalence relation"?

In the set z of integers, define mRn if m-n is div7 , prove that R is an equivalence relation.

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.

Show that the relation R in the set Z of intergers given by R ={(a,b):2 divides a-b } is an equivalence relation.

Show that the relation R in the set A of points in a plane given by R = {(P , Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set o