I'm kinda confused regarding predicate quantifiers.
Firstly, what's the difference between
$\forall x .Tourist(x)$ and $\forall x \in Tourists$
I mean I understand that the first is a predicate form and the second implies that it belongs in the Tourist set but is there a specific case I should be using each one?
Additionally is $\forall x.Tourist(x).\exists y.Country(y).Likes(x,y)$ the same as:
$\forall x\exists y.Tourist(x) \land Country(y) \implies Likes(x,y)$ ??
If not what's the difference?
I'm really struggling to understand these things.
Any help would be much appreciated!