Predicate logic: is this notation correct?

Hey jellies,

I’ve got some homework on predicate logic and I’m wondering if I’m doing it right. Please don’t give me any answers, I’m just unsure about my syntax, basically.

I’m supposed to be translating English sentences into quantifiers. Here’s an example:

There is a student in the calculus class who is neither a math major nor a freshman.

I first defined my universe as being the calculus class, and a predicate P(s, c, m) as “student s is in class year c and majors in m.”

Then I translated the sentence like so:

∃s ¬(P(s, freshman, m) V P(s, c, math))

Which in my head reads “There exists a student s for whom is is not that case that student s is a freshman majoring in m or student s is in class year c majoring in math.”

But I’m thinking this isn’t right because you can’t just leave certain parameters in the predicate as variables to indicate that they can be anything (for example, in P(s, freshman, m) I was trying to indicate that the only parameter that matters/is known about the student is that he is a freshman).

Some pointers?