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  4. If A= .1,2,3,4. , then a relation R= .(.1,1.),(.2,2.),(3 , 3),(.4,4.),(.2,4.),(.1,3.),(.1,4.),(.1,2.). on set A is

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Q. If $A=\left\{\right.1,2,3,4\left.\right\}$ , then a relation $R=\left\{\right.\left(\right.1,1\left.\right),\left(\right.2,2\left.\right),\left(3 , 3\right),\left(\right.4,4\left.\right),\left(\right.2,4\left.\right),\left(\right.1,3\left.\right),\left(\right.1,4\left.\right),\left(\right.1,2\left.\right)\left.\right\}$ on set $A$ is

NTA AbhyasNTA Abhyas 2022

Solution:

$\because \left(\right.2,4\left.\right)\in R$ and $\left(\right.4,2\left.\right)\notin R$
$\therefore $ not-symmetric and $\left(\right.1,2\left.\right),\left(\right.2,4\left.\right)\in R\Rightarrow \left(\right.1,4\left.\right)\in R$
$\therefore $ Transitive
$\because \left(\right.a,a\left.\right)\in R\forall a\in A\Rightarrow $ reflexive
$\therefore R$ is reflexive and transitive.