I am trying to learn the theory behind first-order logic (FOL) and do some practice runs of converting statements into the form of FOL.
One issue I keep running into is hesitating on whether to use an AND ($\land$) statement or an IMPLIES ($\rightarrow$) statement.
I have seen examples such as "Some boys are intelligent" turned into:
$$ \exists x \text{boys}(x) \land \text{intelligent}(x) $$
Can I make a general assumption that when I see $x$ is/are $y$, I can use an AND?
With a statement such as "All movies directed by M. Knight Shamalan have a supernatural character", I feel that that statement can be translated to either:
$$ \forall x, \exists y \; \text{directed}(\text{Shamalan}, x) \rightarrow \text{super-natural character}(y) $$
or
$$ \forall x, \exists y \; \text{directed}(\text{Shamalan}, x) \land \text{super-natural character}(y) $$
Is there a better way to distinguish between when to use one or the other?
∃x boys(x) ∧ intelligent(x)
is correct for the statement "Some boys are intelligent". there might be some boys who aren't intelligent, for which the predicate fails. $\endgroup$