question.md

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

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

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

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