Question

If relation $R$ is defined as $aRb$ if "$a$ is the father of $b".$ Then $R$ is

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

Answer 1

The correct option is D none of these

Given
$R=\left\{\right(a,b);a$ is the father of $b\}$
$\left(i\right)\because (a,a)\notin R$ [as $a$ can not be father of $a$]
So, $R$ is not reflexive.

$\left(ii\right)$ Now if $aRb$ is true, then $a$ is the father of $b\}$
$\Rightarrow (b,a)\notin R$
[as $b$ cannot be father of $a$]
So, $R$ is not symmetric.

$\left(iii\right)$ Let $(a,b)\in R$ and $(b,c)\in R$
Hence $a$ is father of $b$ and $b$ is father of $c$
$\Rightarrow (a,c)\notin R$
[as $a$ is not the father of $c$]
So, $R$ is not transitive.