Question

Let \(\rho\) be a relation defined on \(\mathbb{N}\), the set of natural numbers, as
\(\rho=\{(x, y) \in \mathbb{N} \times \mathbb{N}: 2 x+y=41\}\) 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 1

Ans: (D)
Hint : \(x \rho y, y \rho z \Rightarrow 2 x+y=41\) and \(2 y+z=41\) which do not imply \(2 x+z=41\)

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