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 Z of integers given by: R = {(x, y): 3x - 3y is an integer } is an equivalence relation. [3] If f: RrarrR defined by f(x) = (6- 5x)/7 is an invertible function, find f^-1 .

Prove that the relation R in Z of integers given by: R = {(x, y): x - y is an integer } is an equivalence relation. [3] If f: RrarrR defined by f(x) = (3- 2x)/4 is an invertible function, find f^-1 .

Prove that the relation R in Z of integers given by: R = {(x, y): 2x - 2y is an integer } is an equivalence relation. [3] If f: RrarrR defined by f(x) = (4- 3x)/5 is an invertible function, find f^-1 .

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 on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

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.

Let R be the relation in the set Z of all integers defined by R= {(x,y):x-y is an integer}. Then R is

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

Solve that the relation R in the set z of intergers given by R={(x,y):2 divides (x-y)} is an equivalence relation.