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

Prove that the relation R on Z defined by (a,b)in R hArr a-b is divisible by 5 is an equivalence relation on Z .

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b):|a b | is divisible by 2} is an equivalence relation.Write all the quivalence classes of R .

Show that the relation R in R defined as R={(a,b):ageb} is transitive.

Prove that the relation R in the set A={5,6,7,8,9} given by R={(a,b):|a-b|, is divisible by 2}, is an equivalence relation.Find all elements related to the element 6.

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 integers, given by R = {(a, b): 3 divides a − b} is an equivalence relation. Hence find the equivalence classes of 0, 1 and 2.

The relation R defined in N as aRbimpliesb is divisible by a is

If the relation R in a set of integers defined as R = {(a, b): (a + b) is divisible by 7}, is an equivalence relation, then the equivalence class containing 0 is: