Consider the non-empty set consisting of children in a family and a relation $R$ defined as $aRb$, if $a$ is brother of $b$. Then, $R$ is

transitive but not symmetric

The correct answer is Option (2) → transitive but not symmetric ##

Given, $aRb \Rightarrow a$ is brother of $b$

$∴aRa \Rightarrow a$ is brother of $a$, which is not true.

So, $R$ is not reflexive.

$aRb \Rightarrow a$ is brother of $b$.

This does not mean $b$ is also a brother of $a$ and $b$ can be a sister of $a$.

Hence, $R$ is not symmetric.

$aRb \Rightarrow a$ is brother of $b$

and $bRc \Rightarrow b$ is brother of $c$.

So, $a$ is brother of $c$.

Hence, $R$ is transitive.