Question

Let R be the relation on Z defined by R = {(a, b): a, $bϵZ^2,a-b$ is an integer}. Find the domain and range of R.

Answer 1

Here $R=\left\{\right(a,b):a,bϵZ,a-b$ is an integer}

$=\left\{\right(a,b):a,bϵZ,$ both a and b are even or both a and b are odd}

$=\left\{\right(a,b):a,bϵZ,$ (a and b are even) $\cup$ (a, and b are odd)}

$\therefore$ Domain of R = Z

Range of R = Z