I need to translate an English sentence including the phrase "all but one" into predicate logic. The sentence is: "All students but one have an internet connection." I'm not sure how to show "all but one" in logic.
I could say $\forall x ((x \neq a) \rightarrow I(x))$
$I(x)$ being "$x$ has an internet connection"
But that clearly wouldn't work in this case, as we don't know which student it is.
I could say that $\exists x(\neg I(x))$
But it doesn't seem like that has the same meaning. Thanks in advance for any help you can give!