Question

If a relation $R$ is defined on the set of integers as follows: $(a,b)\in R\iff a^2+b^2=25$. Then domain of $R$ is

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

Answer 1

The correct option is C $\{0,\pm 3,\pm 4,\pm 5\}$

$(a,b)\in R\iff a^2+b^2=25\iff b=\pm \sqrt{25-a^2}$ and $a,b\in I$
$\therefore a=0\Rightarrow b=\pm 5$
$\therefore a=\pm 3\Rightarrow b=\pm 4$
$\therefore a=\pm 4\Rightarrow b=\pm 3$
$\therefore a=\pm 5\Rightarrow b=0$

$\therefore \text{Domain}=\{0,\pm 3,\pm 4,\pm 5\}$