Predicates
$\text{drinks}(p)$: “Person $p$ drinks wine.”
$\text{single}(q)$: “Person $q$ is single.”
English sentence
“Single people drink wine.”
Translations
Which one of the two translations to FOL below is correct?
$\forall p (\text{single}(p) \rightarrow \text{drinks}(p))$, or $\exists p (\text{single}(p) \wedge \text{drinks}(p))$
The proposition “Single people drink wine.” can also be written as “If a person is single, then it drinks wine.”. Therefore, for a person, say $p$, we have that $\text{single}(p) \rightarrow \text{drinks}(p)$. Note that this reasoning works with any person that we pick. I. e. we are not stating anything specific about some person (for that one would usually have some word regard existence in the proposition). So, $\forall p (\text{single}(p) \rightarrow \text{drinks}(p))$. To have $\exists p (\text{single}(p) \wedge \text{drink}(p))$, one should have “There is a single person who drinks.”.