The statement is $$\lnot((\lnot P \land Q) \lor \lnot(R \land \lnot S))$$ and the answer is $$(p \land r) \lor (p \land \lnot s) \lor (\lnot q \land r) \lor (\lnot q \land \lnot s)$$ according to the dCode Boolean Expressions Calculator.
I'm trying to get to the solution myself but I got stuck. I don't know what else to do past what I've done below:
- Start with $\lnot((\lnot P \land Q) \lor \lnot(R \lor \lnot S))$
- De morgan's law $\lnot(\lnot P \land Q) \land \lnot(\lnot(R \lor \lnot S))$
- De morgan's law $\lnot(\lnot P) ∨ \lnot Q \land \lnot(\lnot(R \lor \lnot S))$
- Double negation law $P \lor \lnot Q \land R \lor \lnot S$
- Distributive laws $(P \lor \lnot Q) \land (P \lor \lnot R) \lor \lnot S$