proposition with quantifier 5

Question

I was asked to give an example of a proposition with a quantifier which is true if the quantifier ranges over the integers, but false if it ranges over the rational numbers.

My attempt:

$(\forall n \in \mathbb{Z}, n^2\geq n)$

Is this what the question is looking for?

Answer 1

Here is an example,

$$(\forall (n,p)\in \Bbb N^2)\;\; p\notin (n,n+1)$$

this is not true in $\Bbb Q$ since it is dense.