(Solved): 5. Use De Morgan's Laws (and other logical equivalences) to explain why the following formula is co ...

5. Use De Morgan's Laws (and other logical equivalences) to explain why the following formula is correct: \[ \neg(\neg P \vee \neg Q)=(P \wedge Q) \text {. } \] 5 6. Consider the following quantified statement: \[ \forall x \in U, x^{2}+x=0 \] Write down a (non-empty) Universal Set, \( U \), that makes this a true statement.