Problem: Prove $p rightarrow (q vee r), neg q, neg r vdash neg p$ using Modus Tollens.
I need to prove the validity of the above sequent by using natural deduction. Initially, I didn’t read the entire problem, and went the long way by doing an implication-elimination, two negation-eliminations, an or-elimination, and finally a negation-introduction. Then I read the problem and realized I had to use MT, and now I’m stuck. I don’t have the greatest grasp on propositional logic and natural deduction. Am I allowed to do the following?
Since I have $neg q$ and $neg r$ as my premises, can I use an and-introduction and do $neg q wedge neg r$, which would allow me to immediately use MT to deduce $neg p$? If not, could someone point me in the correct direction? Thanks.