Logic-Kenneth Rosen (Ex1.4-11f) [closed]

Question

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 instead of or in 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.

Please help.

Comments

There is not much difference and both expression are correct I think

Still

∃x ( (S(x) ^ ∀y ( F(y) → A(x,y) ) ) that u can think like this " there exists a student for every faculty member, where student asked a question to faculty member"

 ∀y ( (F(y) → ∃x ( S(x) v A(x,y) ) ) here it means "For every faculty member there exists a student , who asked them a question"

So, logically I think second one is better

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Your formula is absolutely correct. The One given in Rosen and the one with the modification of "And" instead of "Or"..Both are wrong for the given Statement.

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@Sreshtha-I think it depends on what interpretation we take of the statement.

A very good explanation has been given here :

https://math.stackexchange.com/questions/2817200/writing-english-statement-into-predicate-logic-using-quantifiers

@Deepak-you seem to be right about it.

Thank you both Deepak and Srestha

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yes, I missed $\Lambda$ and v portion