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 RhArr a-b is divisible by 5 is an equivalence relation on Z .

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

Let Z be the set of all integers and R be the relation on Z defined by 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 on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

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

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

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

Statement-1: On the set Z of all odd integers relation R defined by (a, b) in R iff a-b is even for all a, b in Z is an equivalence relation. Statement-2: If a relation R on a set A is symmetric and transitive, then it is reflexive and hence an equivalence relation, because (a, b) in Rimplies(b, a)in R" [By symmetry]" (a, b)in R and (b, a) in Rimplies (a,a)in R " [By transitivity]"

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.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.