WBJEE · Maths · Sets and Relations
Let \(\rho\) be a relation defined on \(N\), the set of natural numbers, as \(\rho=\{(x, y) \in N \times N: 2 x+y=41\} .\) Then
- A \(\rho\) is an equivalence relation
- B \(\rho\) is only reflexive relation
- C \(\rho\) is only symmetric relation
- D \(\rho\) is not transitive
Answer & Solution
Correct Answer
(D) \(\rho\) is not transitive
Step-by-step Solution
Detailed explanation
We have, \(\rho=\{(x, y) \in N \times N: 2 x+y=41\}\) For reflexive, \(\begin{array}{l} x p x \Rightarrow 2 x+x=41 \\ \Rightarrow 3 x=41 \end{array}\) \(\Rightarrow x=\frac{41}{3} \notin N\) So, \(\rho\) is not reflexive. For symmetric, \(x \rho y \Rightarrow 2 x+y=41\) and…
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