Natural deduction - formal proof troubles

Question

I'm pretty new to the topic of natural deduction using the Fitch method. I found a very helpful site (http://proofs.openlogicproject.org/) in which you can construct your proofs, but I'm having a lot of trouble with the following:

What I have so far

I get as far as the proof for P but I'm not sure how to then use P to further the proof. I've done a lot of scouring on the net but I just cannot figure out how to continue. Any help would be appreciated.

Thanks

Answer 1

Hint

From $P \land Q$ you have correctly derived both $P$ and $Q$.

Now use $Q$ with $Q \to R$ to derive $R$ and conclude with $P \to R$ by $\to$-intro.

The same wit the other disjunct, in order to use $\lor$-elim to conclude with $P \to R$.

Answer 2

Instead of getting to $P$, try to get to $P \rightarrow R$ in both subproofs, so that you can pull that out using $\lor \ Elim$

To get $P \rightarrow R$, do a subproof within the subproof, where you assume $P$, and get to $R$. You can then end the subproof, and conclude $P \rightarrow R$. So you need to do this within each subproof.

Another option is to immediately start your proof by assuming $P$, and then within that subproof do your two subproofs, trying to get to $R$ in both cases.