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

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.

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.

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

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

A relation R is defined in the set Z of integers as follows (x, y ) in R iff x^(2) + y^(2) = 9 . Which of the following is false ?

Show that the relation R in the set of all integers, Z defined by R = {(a, b) : 2 "divides" a - b} 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.