$ S(x) $ is the predicate "$x$ is a student"
$F(x)$ is the predicate "$x$ is a faculty member"
$A(x,y)$ is the predicate $x$ asked $y$ a question
I need to translate this sentence into logic: Some students asked every faculty member a question.
This is the answer: $\forall y(F(y) \longrightarrow \exists x(S(x) \vee A(x,y))) $
It seems to translate into: For all $y$, if $y$ is a faculty member, then there is some $x$ where $x$ is either a student or $x$ asks $y$ a question. This means that it's possible for $x$ to not be a student, but this makes no sense. I would replace $\vee$ with $\wedge $, would I be wrong?
My second question iswhether the following would also be correct, assuming the first answer is right:
$\exists x(S(x) \longrightarrow \forall y(F(y) \vee A(x,y)))$
There exists an $x$ where if $x$ is a student, then for all $y$ where $y$ is a faculty member, or (I still think it makes more sense if you plug and and here) $x$ asks $y$ a question. It seems to say the same thing.