I've read some examples about the differences between using AND and the implication in FOL, but I have a specific example where I can't intuitively notice the difference between the two:
"Every student able to solve every logic exercise will get an A in AI"
I see that the solution is:
$\forall X\ [\forall P\ exercise(P)\implies solves(X,P)]\implies getsAasgrade(X)$
and I don't understand what's the difference with:
$\forall X\ \forall P\ exercise(P)\cap solves(X,P)\implies getsAasgrade(X)$
since I would read the latter as "for every P which is an exercise and for every entity X such that X solves every exercise P then this entity X gets A", which seems fine to me, but I guess it shouldn't be. Instead I would never express my problem as a nested implication, I really don't even understand how to "read" it in natural language.