Question

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

Answer 1

Compute the required value:

$R$ is the relation on $Z\left(\text{integer}\right)$ defined by $R=\left\{(a,b):a,b\in Z,a–bisaninteger\right\}$.

Since the difference between the two integers is also an integer.

Thus, $a-b$ is an integer.

Hence, the domain of $\mathbf{R}\mathbf{}\mathbf{is}\mathbf{}\mathbf{Z}$ and the range of $\mathbf{R}\mathbf{}\mathbf{is}\mathbf{}\mathbf{Z}$.