Nested quantifiers - Discrete Maths exercise
I'm a little confused about the following exercise:
Let S(x) be "x is a student", F(x) be "x is a faculty member" and A(x,y) be "x has asked y a question"
The domain is "all people associated with your school".
Use quantifiers to express each of these statements
The predicate is: Some student has not asked any faculty member a question
I've found this solution on the web$$ \exists x \forall y {\big(}( F{\small(x)}\land S{\small(y)}) \implies \lnot A{\small(x,y)} {\big)} $$I'd have translated this predicate in the following way:$$ \exists x \forall y {\big(}F{\small(x)}\land (S{\small(y)}\implies\lnot A {\small(x,y)}){\big)} $$Do you think that first solution is correct?
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$\begingroup$The "solution" you quoted from the web is nonsense. Your own solution would be right if you just interchanged $F$ and $S$. As it stands, it says there is a faculty member who hasn't asked any student a question.
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