WBJEE · Maths · Sets and Relations
On the set \(R\) of real numbers, the relation \(\rho\) is defined by \(x \rho y,(x, y) \in R\)
- A If \(|x-y| < 2\), then \(\rho\) is reflexive but neither symmetric nor transitive.
- B II \(x-y < 2\), then \(\rho\) is reflexeve and symmetric bu not transitive.
- C \(If(x \mid \geq y,\) then \(\rho\) is reflexive and transitive but not symmetric.
- D If \(x>|y|\), then \(p\) is transitive but neither reflexve nor symmetric.
Answer & Solution
Correct Answer
(D) If \(x>|y|\), then \(p\) is transitive but neither reflexve nor symmetric.
Step-by-step Solution
Detailed explanation
On the set \(R\) of real numbers For reflexive, \(x \rho x \Rightarrow(x, x) \in R\) \(\Rightarrow x > |x|\) which is not true. \(\Rightarrow \rho\) is not reflexive. For symmetric, \((x, y) \in R \Rightarrow x > |y|\) and \((y, x) \in R \Rightarrow y > |x|\) So,…
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