English to predicate- and vs imply

Question

"Some student in this class hass taken a course in java". First we decided that U is domain. we defined S(x) to be x is student in class. And J(x) to be x has taken java. The solution is :$\exists$ x(S(x) $\land $J(x)) But why $\exists$ x(S(x) $\rightarrow$ J(x)) is not correct, and how is it translated to english.

Answer 1

The assertion $\exists x (S(x)\to J(x))$ would translate to English as "There exists some $x$ such that if $x$ is a student, then $x$ has taken a course in Java." This is not the same as the desired assertion, as there is no guarantee that such $x$ is a student, so it remains possible for no student in the class to have taken a course in Java.

If you really want to pursue this idea, you could write something like $\exists x( S(x) \land (S(x)\to J(x)))$, but this is somewhat silly.