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

Show that the relation R defined by R = {(a, b) (a - b) , is divisible by 5, a, b in N} is an equivalence relation.

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

If R is a relation in N xx N , show that the relation R defined by (a, b) R (c, d) if and only if ad = bc is an equivalence relation.

Show that relation R in Z of integers given by R = {x,y} : x - y is divisible by 5, x , y inZ } 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 integers given by R = {(a, b) : 2 divides a – b} is an equivalence relation.

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 3 divides abs(a-b)} is an equivalence relation.

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 4 divides abs(a-b)} is an equivalence relation.

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 5 divides abs(a-b)} is an equivalence relation.

Prove that the relation R defined in the set A= { x: x in Z, 0 le x le 12} as R = {(a, b) : abs(a-b) . is divisible by 3} is an equivalence relation.