# Prove tautology using propositional equivalence and the laws of logic determine

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

## 1 Answer

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!