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!!!

Recall that $p \def\if{\leftrightarrow}\def\imp{\rightarrow}\if q$ is equivalent to $(p\imp q) \land (q \imp p)$, hence 
$$ \neg (p\if q)\iff \neg(p\imp q) \lor \neg(q\imp p) $$
As $(p \imp q)$ is $\neg p \lor q$, we have 
$$ \neg(p\imp q) \iff p \land \neg q $$
therefore 
$$ \neg (p\if q) \iff (\neg p\land q)\lor (\neg q \land p) $$
distributivity of $\lor$ over $\land$ and $p \lor \neg p \iff 1$ gives 
$$ \neg (p\if q) \iff (\neg p \lor \neg q)\land (p\lor q)\iff (p\imp\neg q) \land(\neg q \imp p) $$
Therefore
$$ \neg (p\if q) \iff (\neg q \if p) $$
