Question

If a relation R is defined on the set Z of integers as follows:
(a, b) ∈ R ⇔ a² + b² = 25. Then, domain (R) is
(a) {3, 4, 5}
(b) {0, 3, 4, 5}
(c) {0, ± 3, ± 4, ± 5}
(d) none of these

Answer 1

(c) {0, ± 3, ± 4, ± 5}

$$\begin{gathered} R=\left\{\left(a,b\right):a^2+b^2=25,a,b\in Z\right\} \\ \Rightarrow a\in \left\{-5,-4,-3,-2,-1,0,1,2,3,4,5\right\}\mathrm{and} \\ b\in \left\{-5,-4,-3,-2,-1,0,1,2,3,4,5\right\} \end{gathered}$$

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