WBJEE · Maths · Sets and Relations
On \(R\), a relation \(\rho\) is defined by xpy if and only if \(x-y\) is zero or irrational. Then.
- A \(\rho\) is equivalence relation
- B \(\rho\) is reflexive but neither symmetric nor transitive
- C \(\rho\) is reflexive and symmetric but not transitive
- D \(\rho\) is symmetric and transitive but not reflexive
Answer & Solution
Correct Answer
(C) \(\rho\) is reflexive and symmetric but not transitive
Step-by-step Solution
Detailed explanation
On the set \(R\) \(x p y \Rightarrow x-y\) is zero or irrational number. Now, \(x p x\) \(\Rightarrow x-x=0\) \(\Rightarrow \rho\) is reflexive. If \(x \rho y \Rightarrow x-y\) is zero or irrational. \(=-(y-x)\) is zero or irrational. \(\Rightarrow\) yox is zero or irrational.…
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