WBJEE · Maths · Sets and Relations
Let the relation \(R_{1}\) be defined on \(R\) as \(a R_{1}b\) if \(1+a b > 0 .\) Then
- A \(R_{1}\) is reflexive only.
- B \(R_{1}\) is equivalence relation.
- C \(R_{1}\) is reflexive and transitive but not symmetric
- D \(R_{1}\) is reflexive and symmetric but not transitive.
Answer & Solution
Correct Answer
(D) \(R_{1}\) is reflexive and symmetric but not transitive.
Step-by-step Solution
Detailed explanation
We observe the following properties: Reflexivity : Let a be an arbitrary element of \(R\), Then, \(a \in R\) \(\Rightarrow 1+a \cdot a=1+a^{2}>0 \quad\left[\because a^{2}>0\right.\) for all \(\left.a \in R\right]\) \(\Rightarrow \quad(a, a) \in R_{1}\) \(\left[\right.\) By def.…
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