The relation S is defined on the set of integers Z as xSy if integer x devides integer y. Then

Show that the relation R defined on the set Z of all integers defined as R={(x,y):x-y is an integer} is reflexive, symmertric and transtive.

Let R be a relation defined on the set Z of all integers and xRy when x+2y is divisible by 3.then

What type of relation does R define on the set of integers, if x+y=8?

Let RR be a relation defined on the set ZZ of all integers and xRy when x+2y is divisible by 3, then

A relation R is defined on the set of all integers Z Z follows : (x,y) in "R" implies (x,y) is divisible by n Prove that R is an equivalence relation on Z Z .

A relation R is defined on the set of integers Z as follows: R{(x,y):x,y in Z and x-y" is odd"} Then the relation R on Z is -

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 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.