WBJEE · Maths · Sets and Relations
For any two real numbers \(\theta\) and \(\phi\) we define \(\theta\). R \(\phi\) if and only if \(\sec ^{2} \theta-\tan ^{2} \phi=1\). The relation \(R\) is
- A reflexive but not transitive
- B symmetric but not reflexive
- C both reflexive and symmetric but not transitive
- D an equivalence relation
Answer & Solution
Correct Answer
(D) an equivalence relation
Step-by-step Solution
Detailed explanation
Given relation is defined as \(\theta R \phi\) such that \(\sec ^{2} \theta-\tan ^{2} \phi=1\) For Reflexive When \(\theta R \theta\) \(\sec ^{2} \theta-\tan ^{2} \theta=1\) \(\Rightarrow 1=1,\) which is true. Thus, it is reflexive. For Symmetric When \(\theta R \phi\)…
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