Difference between these two logical expression

Question

I am trying to solve the following problem:

Let S(x) be the predicate “x is a student,” F(x) the predicate “x is a faculty member,” and A(x, y) the predicate “x has asked y a question,” where the domain consists of all people associated with your school. Use quantifiers to express each of these statements. f ) Some student has asked every faculty member a question.

What is the difference between $\forall y(F(y)\to\exists x(S(x)\land A(x,y)))$ and $\exists x (S(x) \land \forall y(F(y)\to A(x,y)))$? A'int they same?

Answer 1

Hint: Just read it out loud. The first says (simplified): "For every faculty member $y$, there is a student that asked $y$ a question". The second formula reads "There is a student that asked every faculty member a question".

Answer 2

In the first one you are saying: "For every faculty member, there exists a student...", whereas in the second one you are saying: "There is a student, and for all faculty members...". In this question we want the student to be fixed.

Also, the first one seems to actually read: "For all people y, if y is a faculty member then there exists a person x such that x is a student or x has asked y a question".

Answer 3

The first : Every faculty member was questioned by (at least) one student. The second : Some student asked every faculty member....