translating a sentence into predicate calculus

Question

I am supposed to translate the following sentence into predicate calculus:

No Student likes the classroom.

S(x) : x is a student C(x) : x likes the classroom

I am assuming that no Student means none or "not all" so Would I be correct to assume that the translation would be:

¬∀xS(x) -> C(x)

Answer 1

"No student" is not "not all"; it is "all not".

The translation must be :

$∀x(S(x) → ¬C(x))$

which means "if $x$ is a student, then he does not like the classroom", i.e. "no student likes the classroom".

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Your proposed translation :

$¬∀x(S(x) \rightarrow C(x))$

is equivalent to :

$\exists x \lnot (S(x) \rightarrow C(x))$

and thus to :

$\exists x (S(x) \land \lnot C(x))$

that means : "there is some student that does not like the classroom".