# Expressing Quantifications

I have to equations: P(x)=student x knows calculus, and Q(y)=class y contains a student who knows calculus.

For something like "Some students know calculus" would it be enough to write $\exists x P(x)$, or would a better way be $\exists y \exists x Q(y) \wedge P(x)$?

Similarly, to express "every class has a student in it who knows calculus", would it be sufficient to write $\forall y Q(y)$?

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Write "\exists y \exists x Q(y) \wedge P(x)" enclosed within dollar signs to get proper syntax output. – Quinn Culver May 31 '11 at 15:07
For the first question your $\exists x P(x)$ would suffice. And for the second question, indeed what you wrote is sufficient. – Apostolos May 31 '11 at 15:27
@Apostolos, please write your comment as an answer so I can give you credit. And thanks! – Horace May 31 '11 at 15:28
To get $\forall$ you can enclose \forall in dollar signs. – Ross Millikan May 31 '11 at 15:35

For your first question I think your first expression, that is $\exists x P(x)$ would suffice. Your second candidate is a bit pointless unless you can express the relation between students and classrooms (that is a student belongs to a classroom). If you can express it, then maybe it will be considered a nice addition but I don't think it's required.