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 $R$.

• A. $z,z$
• B. $z^{+},z$
• C. $z,z^{-}$
• D. None of these

Answer 1

The correct option is A $z,z$

Given:

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

As difference of integers are also integers so,

Domain of $R=z$

Range of $R=z$, as

$a-b$ spans the whole integer values.