Question

Let $R$ be a relation on the set $N$ be defined by $\{(x, y) \mid x, y \in N, 2 x+y=41\}$. Then $R$ is

(A) Reflexive

(B) Symmetric

(C) Transitive

(D) None of these

Answer 1

$2 x+x=41 \Rightarrow x=\frac{41}{3} \notin N \quad \therefore \quad R$ is not reflexive

$2 x+y=41 \quad \Rightarrow \quad 2 y+x=41 \quad \therefore \quad R$ is not symmetric

$2 x+y=41 \quad$ and $\quad 2 y+z=41 \quad \Rightarrow \quad 4 x-z=41 \Rightarrow(x, z) \notin R$

$\therefore \quad \mathrm{R}$ is not transitive

Above Correct Answer is Option D.