Prove tautology using propositional equivalence and the laws of logic determine

Question

q ∧ ( p → ¬q) → ¬p
q ∧ ( ¬p ∨ ¬q) → ¬p
(q ∧ ¬p)∨ (q ∧ ¬q) → ¬p
(q ∧ ¬p)∨ F → ¬p

i dont know how to solve this further. Kind of leaves me confused what would be the next step

Answer 1

First, a term like $P \lor F$ is equivalent to just $P$. So, as the next step you get:

$(q \land \neg p) \to \neg p$

And now rewrite this second implication just as you did the first. That is, the next step is:

$\neg (q \land \neg p) \lor \neg p$

Now do DeMorgan and you're almost there!