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. ${\forall\,x\;\;} {Smart}(x) \lor (xx)$.
1. $(\exists x\ xx) {\:\;{\Rightarrow}\:\;}({\forall\,y\;\;} \exists z\ yz)$.
2. ${\forall\,x\;\;} P(x) \lor \lnot P(x)$.
3. ${\forall\,x\;\;} {Smart}(x) \lor (xx)$.
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. ${\forall\,x\;\;} {Smart}(x) \lor (xx)$.