WBJEE · Maths · Sets and Relations
For any two real numbers \(a\) and \(b\), we define \(a R b\) if and only if \(\sin ^{2} a+\cos ^{2} b=1\). The relation \(R\) is
- A reflexive but not symmetric
- B symmetric but not transitive
- C transitive but not reflexive
- D an equivalence relation
Answer & Solution
Correct Answer
(D) an equivalence relation
Step-by-step Solution
Detailed explanation
Let the given relation defined as \(R=\left\{(a, b) \mid \sin ^{2} a+\cos ^{2} b=1\right\}\) For reflexive, \(\sin ^{2} a+\cos ^{2} a=1\) \(\left(\because \sin ^{2} \theta+\cos ^{2} \theta=1, \forall \theta \in R\right)\) \(\Rightarrow { }_{a} R_{a} \Rightarrow(a, a) \in R\)…
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