Discrete question. Prove that two propositions are logically equal. I have a question about bi conditional equivalencies and how to prove that they are logically equivalent.
The question states, show that $\neg\;(p \leftrightarrow q)$ and $p \leftrightarrow\neg\; q$ are logically equivalent.
I tried multiple approaches using several laws from left side or right side but I can't find the right path that leads to the right answer. Any ideas?
Please help
Thanks in advance!!!

$p \leftrightarrow q$ is true iff $p$ and $q$ have the same truth-value, and thus:
$\neg(p \leftrightarrow q)$ iff 
$p$ and $q$ do not have the same truth-value iff
$p$ and $q$ have opposite truth-values iff
$p$ and $\neg q$ have the same truth-value iff
$p \leftrightarrow \neg q$
