Explanation

(d)
Since, $R$ is defined as $aRb$ iff $|a - b| > 0$.
Reflexive : $aRa$ iff $|a - a| > 0$
Which is not true. So, $R$ is not reflexive.
Symmetric : $aRb$ iff $|a - b| > 0$
Now, $bRa$ iff $|b - a| > 0$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |a - b| > 0\ \ \ \ \Rightarrow \ \ \ aRb$
Thus, $R$ is symmetric.
Transitive : $aRb$ iff $|a - b| > 0$
$bRc$ iff $|b - c| > 0$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |a - b + b - c| > 0$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |a - c| > 0$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |c - a| > 0 \Rightarrow aRc$
Thus, $R$ is also transitive.