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

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

$aRa \Rightarrow a$ 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 we can say that, $R$ is not symmetric.
$aRb \Rightarrow a$ is brother of $b$

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

So, $a$ is brother of $c$.
Hence we can say that, $R$ is transitive.