Prove $R \lor P \Rightarrow S$ given the following premises?

Question

I'm having issues with proving $R \lor P \Rightarrow S$, given the following premises:

1. $P \Rightarrow Q$,
2. $\neg P \land R \Rightarrow S$,
3. $\neg Q$.

Any help is appreciated.

Answer 1

It depends on what system you want to use. I will try to give a general idea of the proof.

1. $(\neg Q)$ and $ (P \Rightarrow Q) $ imply $ \neg P$ (why? can you prove this?)
2. $ \neg P $ together with $ (R \lor P) $ imply $ R $ (again, can you prove this?)
3. finally $ \neg P, R $ and $ \neg P \land R \Rightarrow S $ obviously imply $S$.