Question

Let R be the relation on Z defined by R = {(a, b): a, b $\in$ Z a - b is an integer}. Find the domain and range of R.

• A. Domain of R = ∅ Range of R = ∅
• B. Domain of R = Z, Range of R = Z
• C. Domain of R = {1, 2, 3, 4, 5} Range of R = {0, 1, 2, 3, 4, 5}
• D. None of these

Answer 1

The correct option is B

Domain of R = Z, Range of R = Z

R = {(a, b): a, b $\in$ Z, a - b is an integer}

It is known that the difference between any two integers is always an integer.

$\therefore$ Domain of R = Z, and Range of R = Z
Domain and Range both will be real numbers.