Sufficient conditions for De Morgan's law in intuitionistic logic

Question

What are the sufficient conditions for De Morgan's law $\lnot(P\wedge Q)\Rightarrow \lnot P \vee \lnot Q$ in intuitionistic logic?

If $P\vee \lnot P$ and $Q\vee \lnot Q$ are true, is it true?

Answer 1

Yes. Under that assumption, you can examine the four cases. In three of the cases either $\lnot P$ or $\lnot Q$ holds, then $\lnot P\lor \lnot Q$ holds you're done. In the other case, $P\land Q$ holds, and this contradicts the premise.