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  4. If R is a relation on the set N , defined by .(.x,y.):2x-y=10. , then R is

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

NTA AbhyasNTA Abhyas 2022

Solution:

$\because \left(\right.x,x\left.\right)\notin R$
$\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