Question

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

Answer 1

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

We know that the difference of any two integers is always an integer.

Thus, for all $a,b\in Z,$ we get $a-b$ is an integer.

Therefore,

Domain $=Z$ and Range $=Z$