Question

Define a relation R from Z to Z, given by 

R = {(a, b): a, b ϵ Z and (a – b) is an integer. 

Find dom (R) and range (R).

Answer 1

Given: R = {(a, b): a, b ϵ Z and (a – b) is an integer 

The condition satisfies for all the values of a and b to be any integer. 

So, R = {(a, b): for all a, b ϵ (-∞, ∞)} 

Dom(R) = {-∞, ∞} 

Range(R) = {-∞, ∞}