Exercise 8.7 [nqueens-size-exercise]

Which of the following are valid (necessarily true) sentences?

1. $(\exists x\ xx) {:\;{\Rightarrow}:\;}({\forall\,y\;\;} \exists z\ yz)$.

2. ${\forall\,x\;\;} P(x) \lor \lnot P(x)$.

3. ${\forall\,x\;\;} {Smart}(x) \lor (xx)$.