Translating a statement into a logical expression for two different domains.

Question

I am given a statement like the following:

Everyone in your class has a cellular phone

I need to represent this twice, once for a domain of consists of the students in your class and once for consists of all people

This is confusing me because it looks like the given statement is worded in a way to only work for the first domain. I believe I have the first domain down:

Let $P(x) = $ "x has a cellular phone"

$\forall x P(x)$

However then how would the second one look? I feel like since the domain is changed now, it would be the exact same thing? Or am I messing this up?

Answer 1

Introduce a predicate $C(x)$ that is interpreted as "$x$ is in your class."

Then the sentence you want is: $$\forall x (C(x) \rightarrow P(x))$$

Answer 2

Hint: conditionals . . .

Longer hint: it might be easier to first express "It is not the case that every student in your class has a phone."