Question

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

Answer 1

Given $R=\left\{\right(a,b):a,b\in Z,a-b$ is an integer$\}$
$a\in Z$ So, Domain of $R$ is $Z$.

$R$ is such that $a-b\in Z$ and we have $a\in Z$ so $b\in Z.$
So, Range of $R$ is $Z$.

$\therefore$ Domain of $R=Z$ and Range of $R=Z.$