# If a relation R is defined on the set Z of integers as follows:

Question:

If a relation R is defined on the set Z of integers as follows:

$(a, b) \in R \Leftrightarrow a^{2}+b^{2}=25$. Then, domain (R) is

(a) $\{3,4,5\}$

(b) $\{0,3,4,5\}$

(c) $\{0, \pm 3, \pm 4, \pm 5\}$

(d) none of these

Solution:

(c) $\{0, \pm 3, \pm 4, \pm 5\}$

$R=\left\{(a, b): a^{2}+b^{2}=25, a, b \in Z\right\}$

$\Rightarrow a \in\{-5,-4,-3,-2,-1,0,1,2,3,4,5\}$ and

$b \in\{-5,-4,-3,-2,-1,0,1,2,3,4,5\}$

So, domain $(R)=\{0, \pm 3, \pm 4, \pm 5\}$