If a relation R is defined on the set Z of integers as follows:
$(a, b) ∈R⇔a^2+b^2 = 25$. Then, Domain (R) =
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → {0, ±3, ±4, ±5}
We have,
$(a, b)∈R⇔a^2+b^2 = 25⇔b=±\sqrt{25-a^2}$
Clearly, $a = 0 ⇒ b=±5, a=±3 ⇒ b=±4$
$a=±4 ⇒b = ±3$ and, $a = ±5⇒ b=±0$
Hence, domain (R) = $\{a: (a, b) ∈ R\} = \{0,±3, ±4, ±5\}$.