Predicate Logic - Translate the following statement into the notation of predicate

Question

Question: Translate the following statement into the notation of predicate logic.

P: Not all natural numbers are even.
My solution:
P: ~[∀x ∈ N, x/2 ∉ Z]
P: ∃x ∈ N, x/2 ∈ Z

Is my solution correct as my answer seems to be completely different to what is says in the worksheet.

Answer 1

I would not use the division, which is not an internal operation in the integers. Hence I would write : $$ \exists x\in\mathbb{N},\forall y\in\mathbb{N}\quad x\not=2y. $$

Answer 2

You could express it this way:

$$\sim[\forall n \in \Bbb{N}, \exists m \in \Bbb{N}, 2m = n]$$