Let R be the relation in the set Z of integers given by R={(a,b):2 divides a-b}. Show that the relation R transitive ? Write the equivalence class [0].

Show that the relation R on the set Z of integers,given by R={(a,b):2 divides a-b}, 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.

Let R be the relation in the set N given by R = {(a,b):|a-b| is odd}. Then:

Let R be the equivalence relation in the set Z of integers given by R={(a,b):2 divides a-b} .Write the equivalence class of [0]

Let R be the relation in the set N given by R = {a,b):a is a multiple of b} .Then :

Check whether the relation R in the set Z of integers defined as R={(a,b):a +b is divisible by 2} is reflexive, symmetric or transitive. Write the equivalence class containing 0 i.e. [0].

Let R be the relation in the set Z of all integers defined by R= {(x,y):x-y is an integer}. Then R is

Let R be a relation on the set of integers given by aRb hArr a2^(k).b for some integer k. Then,R is