How to use distribution with propositional logic?

Question

I need to apply the distribution rule for propositional logic. I know that the if you have a sentence like $A ∧ (B ∨ C)$ then applying distribution would result in the sentence $(A ∧ B) ∨ (A ∧ C)$. I'm having trouble applying this rule to the following sentence. $(p ∨ q ∨ \neg r) ∧ ((r ∧ \neg q ∧ \neg p) ∨ ((r ∨ q) ∧ \neg q ∧ \neg p))$. So how would I apply distribution to this sentence?

Answer 1

HINT

Start with $$(r\lor q)\land\lnot q= (r\land\lnot q)\lor(q\land\lnot q)=(r\land\lnot q)\lor 0= r\land\lnot q.$$ Plug this in and a big simplification should present itself.