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

In the set z of integers, define mRn if m-n is div7 , 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.

Prove that the relation R defined on the set V of all vectors by vecaRvecbif veca=vecb, is an equivalence relation on V.

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

Show that the relation R in the set R of real numbers, defined as R={(a ,b): alt=b^2} is neither reflexive nor symmetric nor transitive.

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.