WBJEE · Maths · Sets and Relations
A relation \(\rho\) on the set of real number \(R\) is defined as \(\{x \rho y: x y>0\} .\) Then, which of the following is/are true?
- A \(\rho\) is reflexve and symmetric
- B \(\rho\) is symmetric but not reflexive
- C \(\rho\) is symmetric and transitive
- D \(\rho\) is an equivalence relation
Answer & Solution
Correct Answer
(C) \(\rho\) is symmetric and transitive
Step-by-step Solution
Detailed explanation
We have, \(x p y: x y > 0\) (i) Reflexive Suppose \(x \rho x \in R\) \(\Rightarrow x^{2} > 0\) which is not true when \(x=0\). Hence, relation is not reflexive. (ii) Symmetric \(x p y \in R\) \(\Rightarrow \quad x y>0\) \(\Rightarrow \quad y x>0\)…
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