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) =

• A. $\{ 3, 4 , 5\}$
• B. $\{ 0 , 3, 4 , 5\}$
• C. $\{ 0, \pm 3, 4 \pm , \pm 5\}$
• D. $\{ 0 , \pm 5 \}$

Answer 1

Answer: (C)

We have $(a, b) \in R \Leftrightarrow a^2 + b^2 = 25$
$\Leftrightarrow \, b = \pm \sqrt{25 - a^2}$
Clearly , $a = 0 \Rightarrow b = \pm 5$
$ a = \pm 3 \to b = \pm 4$
$ a = \pm 4 \to b = \pm 3$
and $a = \pm 5 \to b = \pm 0 $