If a relation R is defined on the set Z of integers as follows (a, b) ∈ R Leftrightarrow a2 + b2 = 25 , Then , Domain (R) =

Question

If a relation R is defined on the set Z of integers as follows (a, b) ∈ R Leftrightarrow a2 + b2 = 25 , Then , Domain (R) = (A)  3, 4 , 5  (B)  0 , 3, 4 , 5  (C)  0, ± 3, 4 ± , ± 5  (D)  0 , ± 5

Tardigrade Admin · Accepted Answer

We have (a, b) ∈ R Leftrightarrow a2 + b2 = 25 Leftrightarrow b = ± √25 - a2 Clearly , a = 0 ⇒ b = ± 5 a = ± 3 → b = ± 4 a = ± 4 → b = ± 3 and a = ± 5 → b = ± 0

Q. 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) =

${3, 4, 5}$

${0, 3, 4, 5}$

${0, \pm 3, 4 \pm, \pm 5}$

${0, \pm 5}$

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

Q. If a relation R is defined on the set Z of integers as follows (a,b)∈R⇔a2+b2=25 , Then , Domain (R) =

{3,4,5}

{0,3,4,5}

{0,±3,4±,±5}

{0,±5}