Let `R` be the equivalence relation in the set `A={0,\ 1,\ 2,\ 3,\ 4,\ 5}` given by `R={(a ,\ b):2` divides `(a-b)}` . Write the equivalence class [0].

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 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 R is an equivaence relation R defined on the set S={1,2,3,4,5} given by R={(a,b):|a-b| is even } is an equivalence relation .

Show that the relation R in the set A = {1, 2, 3, 4, 5,6,7} given by R = {(a , b) : |a - b| " is even" } , is an equivalence relation.

Let R be the relation in the set A={1,2,3,4} given by R={(a,b):|a-b| is odd number } Write all the elements of R.

Is the relation R in the set A={1,2,3,4,5} defined as R={(a,b):b=a+1} reflexive ?

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b):|a-b| is even }, is an equivalence relation.

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 .

Prove that the relation R in the set A={1,2,3,4,5,6,7} given by R={(a,b):|a-b|iseven} is an equivalence relation.