How do I convert this statement to implication? Or is it not possible?

Question

$$\neg P \land \neg Q \land \neg R$$

The implication may have negations, but no or/and

Answer 1

HINT: Note that $S\lor T$ is equivalent to $\neg(\neg S)\lor T$, which in turn is equivalent to $\neg S\to T$. We can apply De Morgan’s law to see that $\neg P\land\neg Q\land\neg R$ is equivalent to $\neg(P\lor Q\lor R)$. Using the first observation, we see that this is equivalent to $\neg\big(\neg P\to(Q\lor R)\big)$. Can you finish it from here?

Answer 2

\begin{align} \neg P \land \neg Q \land \neg R &= \neg P \land \neg (Q \lor R)\\ &= \neg P \land \neg (\neg Q \Rightarrow R) \\ &= \neg (P \lor (\neg Q \Rightarrow R))\\ &= \neg (\neg P \Rightarrow (\neg Q \Rightarrow R)))\\ &= \neg (\neg P \Rightarrow (\neg Q \Rightarrow R)))\\ \end{align}

You might want to look up Karnuagh maps also