2. Given the following sentences in propositional calculus:
1. $(r \rightarrow u)$
2. $(u \rightarrow \neg w)$
3. $(\neg r \rightarrow \neg w)$
Use resolution refutation to prove $\neg w$.
If it rains, Joe brings his umbrella
If Joe has an umbrella, he doesn't get wet
If it doesn't rain, Joe doesn't get wet
Joe doesn't get wet