Let r be the relation on z defined by R = {( a , b ): a , b ∈ Z , a – b is an integer}. Find the domain and range of R.

Given, r is the relation on Z defined by:

 R={ ( a,b ):a,b∈Z,a−b  is an integer }

To find: Domain and Range of R

Since, the difference of the two integers is also an integer.

Thus, a – b is an integer

Therefore,

Domain of R=Z

Range of R=Z

Hence, Z is an integer.