Question

If $R$ is a relation on the set $N$ , defined by $\{(x,y):2x-y=10\}$ , then $R$ is

• A. reflexive
• B. symmetric
• C. transitive
• D. none of these

Answer 1

Answer: (D)

$\because (x,x)\notin R$
$\therefore$ not reflexive
If $2x-y=10\Rightarrow 2y-x=10$
$\therefore$ not symmetric
If $2x-y=10$ and $2y-z=10$
$\Rightarrow 2x-z=10\therefore$ not transitive