Relation R on Z defined as `R = {(x ,y): x - y "is an integer"}`. Show that R is an equivalence relation.

Let R be the relation on Z defined by aRb iff a-b is an even integer. Show that R is an equivalence relation.

Prove that the relation R in the set of integers Z defined by R = {(x,y) : x - y. is an integer) is an equivalence relation.

Prove that the relation R in the set of integers z defined by R = { ( x , y) : x-y is an integer } is an equivalence relation.

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

A = {(1,2,3,......10} The relation R defined in the set A as R = {(x,y) : y = 2x} . Show that R is not an equivalence relation.

If I is the set of real numbers, then prove that the relation R={(x,y) : x,y in I and x-y " is an integer "} , then prove that R is an equivalence relations.

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.

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.

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.