JEE Mains · Maths · STD 12 - 1. relation and function
Let \(R_{1}\) and \(R_{2}\) be two relations defined on \(R\) by \(a R _{1} b \Leftrightarrow a b \geq 0\) and \(a R_{2} b \Leftrightarrow a \geq b\), then
- A \(R_{1}\) is an equivalence relation but not \(R_{2}\)
- B \(R_{2}\) is an equivalence relation but not \(R_{1}\)
- C both \(R_{1}\) and \(R_{2}\) are equivalence relations
- D neither \(R_{1}\) nor \(R_{2}\) is an equivalence relation
Answer & Solution
Correct Answer
(D) neither \(R_{1}\) nor \(R_{2}\) is an equivalence relation
Step-by-step Solution
Detailed explanation
\(R_{1}=\{x y \geq 0, x, y \in R\}\) For reflexive \(x \times x \geq 0\) which is true. For symmetric If \(x y \geq 0 \Rightarrow y x \geq 0\) If \(x =2, y =0\) and \(z =-2\) Then \(x . y \geq 0 \& y . z \geq 0\) but \(x . z \geq 0\) is not true \(\Rightarrow\) not transitive…
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