WBJEE · Maths · Sets and Relations
On \(R\), the set of real numbers, a relation \(\rho\) is defined as \(a \rho b\) if and only if \(1+a b>0\). Then,
- A \(\rho\) is an equivalence relation
- B \(\rho\) is reflexive and transitive but not symmetric
- C \(\rho\) is reflexive and symmetric but not transitive
- D \(\rho\) is only symmetric
Answer & Solution
Correct Answer
(C) \(\rho\) is reflexive and symmetric but not transitive
Step-by-step Solution
Detailed explanation
We know that, \(1+a^{2}>0, a \in R\) \(\Rightarrow \quad(a, a) \in \rho\) \(\therefore \rho\) is reflexive Again, \(\quad\) let \((a, b) \in \rho\) \(\Rightarrow \quad 1+a b>0\) \(\Rightarrow \quad 1+b a>0\) \(\Rightarrow \quad(b, a) \in \rho\) \(\therefore \rho\) is symmetric…
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