How do I reduce (¬(p ∨ q) ∨ ¬(p ∨ ¬q)) to ¬p using laws of statement logic? I have to reduce 
$(¬(p ∨ q) ∨ ¬(p ∨ ¬q))$
and
$((p ∨ q) ↔ (¬p ∧ q))$
to 
$¬p$
I'm not trying to get someone to do my homework. I'm new to semantics and am having a lot of trouble and the lectures and textbook aren't helping. So I would appreciate any and all guidance. Thank you!

Edit: Thank you so much everyone! @Pé de Leão
For the first one I got the following: 


*

*¬(p∨q)∨¬(p∨¬q)

*(¬p∧¬q)∨(¬p∧¬¬q) DM

*(¬p∧¬q)∨(¬p∧q) Complement

*(¬p∧¬p)∨(¬q∧q) Distributive

*(¬p∧¬p)∨F Complement

*(¬p)∨F Idempotent

*¬p Identity


Is this incorrect?
 A: The first can be simplified as follows:
\begin{array}{l}
& \neg (p \lor q) \lor \neg (p \lor \neg q) & \text{ Given }\\
& (\neg p \land \neg q) \lor (\neg p \land q) & \text{ DeMorgan's law }\\
& \neg p \land (\neg q \lor q) & \text{ Distributive }\\
& \neg p \land T & \text{ Complement }\\
& \neg p & \text{ Identity }\\
\end{array}
Here's the second one:
\begin{array}{l}
& (p \lor q) \iff (\neg p \land q) & \text{ Given }\\
& ((p \lor q) \Rightarrow (\neg p \land q)) \land ((\neg p \land q) \Rightarrow (p \lor q)) & \text{ $\iff$ Elimination }\\
& (\neg (p \lor q) \lor (\neg p \land q)) \land (\neg (\neg p \land q) \lor (p \lor q)) & \text{ Material Implication }\\
& ((\neg p \land \neg q) \lor (\neg p \land q)) \land ((p \lor \neg q) \lor (p \lor q)) & \text{ DeMorgan's law }\\
& ((\neg p \land \neg q) \lor (\neg p \land q)) \land (p \lor p \lor \neg q \lor q) & \text{ Associative }\\
& ((\neg p \land \neg q) \lor (\neg p \land q)) \land (p \lor \neg q \lor q) & \text{ Idempotent }\\
& ((\neg p \land \neg q) \lor (\neg p \land q)) \land (p \lor T) & \text{ Complement }\\
& ((\neg p \land \neg q) \lor (\neg p \land q)) \land T & \text{ Identity }\\
& (\neg p \land \neg q) \lor (\neg p \land q) & \text{ Identity }\\
& \neg p \land (\neg q \lor q) & \text{ Distributive }\\
& \neg p \land T & \text{ Identity }\\
& \neg p & \text{ Identity }\\
\end{array}
A: hint: you can use the law of DeMorgan: \begin{matrix}\neg {(a\wedge b)}=\neg {a}\vee \neg {b}\\\neg {(a\vee b)}=\neg {a}\wedge \neg {b}\end{matrix}
