WBJEE · Maths · Sets and Relations
Le the relation \(\rho\) be defined on \(\mathbb{R}\) by a \(\rho\) b holds if and only if \(a-b\) is zero or irrational, then
- A \(\rho\) is equivalence relation
- B \(\rho\) is reflexive \(\&\) symmetric but is not transitive
- C \(\rho\) is reflexive and transitive but is not symmetric
- D \(\rho\) is reflexive only
Answer & Solution
Correct Answer
(B) \(\rho\) is reflexive \(\&\) symmetric but is not transitive
Step-by-step Solution
Detailed explanation
Hint: If \(a-b=0\) then \(b-a=0\), if \(a-b\) is irrational then \(b-a\) is irrational \(\therefore a \rho b \Rightarrow b \rho a \Rightarrow\) symmetric \(\forall a \in \mathbb{R}, a-a=0 a \rho a \Rightarrow\) reflexive If \(a=2, b=\sqrt{2}, c=3\), then a \(\rho\) b, b \(\rho\)…
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