Below was the exercise problem I was solving from Discrete Mathematics by Kenneth Rosen (for preparation of GATE Exam) and I have doubt in it.
Let S(x) be the predicate that "x is a student", F(x) be 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.
Now my doubt is
it can be framed like there is at least one student such that for all faculty members, he must have asked them a question.
so I wrote my expression as
∃x ( (S(x) ^ ∀y ( F(y) $\rightarrow$ A(x,y) ) )
But in Rosen answer is given as below and I have 2 doubts in it.
Rosen's Ans : ∀y ( (F(y) $\rightarrow$ ∃x ( S(x) v A(x,y) ) )
Doubt 1: I think in above expression we must have "and operator" instead of "or operator" in the second part of expression which is quantified by existential quantifier and so it should be
∀y ( (F(y) $\rightarrow$ ∃x ( S(x) ^ A(x,y) ) )
Doubt 2: What is the difference between my answer and Rosen's answer.Which one is correct.