[" 51.The relation "R" defined in the set "Z" as "R={(x,y):x-y in Z}" show that "R" 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.

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

A relation R is defined on the set of integers Z Z as follows R= {(x,y) :x,y inZ Z and (x-y) is even } show that R is an equivalence relation on Z Z .

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.