Prove using classical logic that $q \to r, r \to p \vdash_c \neg (\neg p \land q)$

Question

Prove using classical logic that $q \to r, r \to p \vdash_c \neg (\neg p \land q)$

Hello, I'm finding hard to prove this...

I've been to use the left implication rule, Modus Tollens, Disjunctive syllogism. But I can not seem to find a way to derivate this...

Can anyone provide help?

Thank you in advance...

Answer 1

Hint

Assume $(\lnot p \land q)$ and use $(\land \text E)$ to derive $\lnot p$ and $q$.

With $q$ derive $p$, using $(\to \text E)$ twice.

Now use $(\to \text E)$ to derive $\bot$ and conclude with $\lnot (\lnot p \land q)$ using $(\to \text I)$.

Note: the names of the rule are those of page 33.