Translating an English statement to it's logical equivalent: "No student is friendly but not helpful" I am curious about the correct interpretation of the following English sentence in predicate logic. I suppose, I may also have to ask an English grammarian.
Let the following predicates be given. The domain consists of all people.
$F(x) = x$ is friendly
$H(x) = x$ is helpful
$S(x) = x$ is a student
Express the following English sentence in terms of $F(x)$, $H(x)$, $S(x)$, quantifiers, and logical connectives.
"No student is friendly but not helpful."
Is it:
A

$¬∃x(S(x) ∧ F(x) ∧ ¬H(x))$
There does not exist a person such that that person is a student, that
person is friendly, and that person is not helpful.

or
B

$∀x( S(x) → (¬F(x)∧H(x))$
that person is not friendly and helpful. For all people if a person is a student then

FOLLOW UP

It may be useful to note the ambiguity in the English, which is clarified by the first comment on my posting to the English Grammar & Usage stack exchange, linked HERE

 A: Note: $\;\neg \big(F(x) \wedge \neg H(x)\big) \iff \big(\neg F(x)\vee H(x)\big)\;$  by DeMorgan's Laws.

Now $\;\neg \exists x\, \big(S(x)\wedge F(x)\wedge \neg H(x)\big)\;$ parses as: "there is nothing that is a student and friendly and not helpful," or more naturally: "no student is friendly and/but not helpful."   Which is what you were required to express.
So applying dual negation, DeMorgan's law, and implication equivalence to this actually produces: $\;\forall x\, \Big(S(x) \;\to\; \big(\neg F(x)\vee H(x)\big)\Big)\;$, which parses as "if anything is a student then it is not friendly or it is helpful," or "any student either is not friendly or is helpful."
Alternatively, the equivalent, $\;\forall x\, \Big(S(x) \;\to\; \neg \big(F(x)\wedge \neg H(x)\big)\Big)\;$, reads, somewhat awkwardly as, "any student is not both friendly and not helpful".
I'd stay with the first form of the expression; as it say what you want in a way that is most compatible with natural language.
A: Notice that when you wrote an English sentence corresponding to A, you had (more or less) the same English sentence with which you began.
Also notice that statement B says that if a person is a student, that person is not friendly, which your original sentence did not imply (and which we hope is not true!).
(This would be more appropriate in a comment, but I haven't the reputation.)
