# Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}.

Question:

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

Solution:

$\mathrm{R}=\{(a, b): a, b \in \mathbf{Z}, a-b$ is an integer $\}$

It is known that the difference between any two integers is always an integer.

$\therefore$ Domain of $R=Z$

Range of $R=Z$