Here are two propositions:
1.∃x(F(x)∧∀yF(y)∧x≠y→A(x,y))
2.∃x∀y(F(x)∧F(y)∧x≠y→A(x,y))
domain of x: the whole body of students and faculty members
domain of y: the whole body of students and faculty members
F(x): x is a faculty member;
A(x,y): x has asked y a question
The expression 1 is supposed to mean in English that "there exists a faculty member who has asked every other faculty member a question."
Personnally I think that the expression 2 means the same thing as expression 1, since there's no y appearing before ∀y, we can drag ∀y out in front. But my TA says the expression is not equivalent. But I don't get how they aren't? We can't drag ∀y in front even though there's no y before it? Why?
edit: as pointed out by @Jair Taylor the expressions are without clarifying parentheses, but I'm assuming that it's like this:
1.∃x{F(x)∧∀y[F(y)∧(x≠y)→A(x,y)]}
2.∃x∀y[F(x)∧F(y)∧(x≠y)→A(x,y)]