Hey guys, I've been banging my head against the wall trying to figure this one out. It's the first problem in my problem set (so it should be one of the easier ones), but I have taken many dead end routes trying to figure this out. The problem is as follows:

1. $\displaystyle (\sim U \rightarrow Z) \rightarrow (Y \wedge \sim B)$

2. $\displaystyle \sim U \rightarrow (H \vee Z)$

3. $\displaystyle H \rightarrow Z$

/ $\displaystyle \sim B$

So far I've been trying to use a conditional to prove $\displaystyle \sim U \rightarrow Z$ so that I can use MP to get $\displaystyle Y \wedge \sim B$, and by simplification $\displaystyle \sim B$ , but everything I've tried thus far is a dead end. Any and all help would be greatly appreciated! Thanks!