Prove using Propositional logic laws | Killer question!

Question

I'm stuck on this for 2 hours. Can't start with R.H.S also due to less no of variables.

Q. $(p \land q \land \neg r) \lor (p \land \neg q \land \neg r) \equiv p \land \neg r$

Here I started:

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

$p \land (q \land \neg r) \lor p \land (\neg q \land \neg r)$ using Associative Law

$p \land (\neg q \land \neg r) \lor p \land (q \land \neg r)$ using Distributive Law

What else can we do with it? Any idea? Much appreciated.

Answer 1

You have $$(p \land q \land \neg r) \lor (p \land \neg q \land \neg r) \equiv p \land \neg r \iff (p\land \neg r)(q\lor \neg q)$$ by invoking the distributive law.