The question asks to convert $\neg(p \lor \neg q) \rightarrow (\neg r \land (p \rightarrow r))$ to a DNF.
I got it till $\neg(\neg p \land q) \lor (\neg r \land \neg p)$. I dont know how to simplify it further. I know that the first clause can be simplified further using DeMorgans but then it would become a disjunct instead of a conjunct. What should I do?
With De Morgan's laws, you get $$(p~\lor~\neg q)~\lor~(\neg r~\land~\neg p)$$ which might be confusing but it actually is in DNF. Why? Note that disjunction (the OR) is associative. This means that for any formulas $A, B$ and $C$, $$(A~\lor~B)~\lor~ C~\equiv~A~\lor~(B~\lor~ C)~\equiv~A~\lor~B~\lor~ C$$
You can use associativity in your formula to remove the confusing parentheses, and then you obtain $$p~\lor~(\neg q)~\lor~(\neg r~\land~\neg p)$$