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

Last updated date: 18th Mar 2023
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Hint: We are given that $R$ is the relation on $Z$ defined by $R=\left\{ (a,b):a,b\in Z,a-b\text{ is an integer} \right\}$. So we know that the difference of integers is always integers. Try it, you will get the answer.

It is given in the question that, $a,b\in Z$.
The relation $R$ on $Z$ is defined by
$R=\left\{ (a,b):a,b\in Z,a-b\text{ is an integer} \right\}$
So, Domain $R$$= Z. Also, range R$$=$ $Z$.