Existential Quantifier translate Translate the following sentence into predicate logic: “Some student in this class has taken a course in Java.” But if U is all people, then translate as                 x (S(x) ∧ J(x))
x (S(x)→ J(x)) is not correct. What does it mean?
 A: I'm assuming the square shape is supposed to be the existential quantifier. For the future, I highly recommend using LaTeX because it lets you easily type the $\exists$, $\land$, and $\to$ symbols.
Anyway, here's the answer:
$\exists x(S(x) \land J(x))$ is correct because it is saying "there exists someone who is a student, and is taking Java", which is equivalent to the original sentence of "Some student in this class has taken a course in Java."
$\exists x(S(x) \to J(x))$ is not correct, because it is saying "there exists someone, such that if they are a student, then they are taking Java". It doesn't actually state that there is a student who satisfies both properties.
If it clarifies things, it's just like the difference between "Someone just had a heart attack and had to go to the hospital!!" and "There is someone such that if that person has a heart attack, then they will have to go to the hospital". The first one will result in an "oh no!" response, the second will result in a rather confused "...duh."
