WBJEE · Maths · Sets and Relations
On \(R\), the relation \(\rho\) be defined by 'xpy holds if and only if \(x-y\) is zero or irrational'. Then,
- A \(\rho\) is reflexive and transitive but not symmetric
- B \(\rho\) is reflexive and symmetric but not transitive
- C \(\rho\) is symmetric and transitive but not reflexive
- D \(\rho\) is equivalence relation
Answer & Solution
Correct Answer
(B) \(\rho\) is reflexive and symmetric but not transitive
Step-by-step Solution
Detailed explanation
We have, \(x p y \Rightarrow x-y\) is zero or irrational. Now, \(x-x=0\) \(\Rightarrow(x, x) \in \rho\) \(\therefore \rho\) is reflexive. Again, if \(x-y\) is either zero or irrational, then \(y-x\) will also be either zero or inational. \((x, y) \in \rho\)…
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