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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 ___________
Options
{3, 4, 5}
{0, 3, 4, 5}
{0, ±3, ±4, ±5}
None of these
Solution
{0, ± 3, ± 4, ± 5}
R={ (a, b) : a2 + b2 =25, a, b ∈ Z }
⇒ a ∈ {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5} and
b ∈ {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5}
So, domain (R)= {0, ±3, ±4, ±5}
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