Rules of inference question help

Question

itiaax · Answer

So I've been working at this question for the longest while, now, but just keep going around in circles and can't figure how to complete it.

I am given these premises
$$-q \rightarrow (r \rightarrow -s)$$
$$-p \rightarrow r$$
$$-q v w $$ (not q or w)
$$-(p v w)$$ (not of p or w)

I must show that the conclusion -s (not s) is valid

blazeryder · Answer

@zepdrix

itiaax · Answer

I'm not sure what you mean by material implication

itiaax · Answer

Oh, I know what you mean now

itiaax · Answer

Okay, I will try again now.

inkyvoyd · Answer

if that doesn't work, lmk... I'm not sure it will since that's usually my first stab at things;

itiaax · Answer

@inkyvoyd  I've did a few things and I'm now left with ~r v s and p v r. I'm unsure of how to go along from here

itiaax · Answer

I turned the first two premises into implications. Turned the ~(p v w) to ~p ^ w using De Morgan's. Simpliied that to ~w. Used disjunctive syllogism twice