Using logical quantifiers to express statement

Question

I'm new to logical quantifiers and not sure if anything I'm doing is right. I'm supposed to give a mathematical expression for the following:

"For every natural number x there is an integer smaller than x such that their product is positive."

I've done ∀x∈N: and that's it. Any help would be appreciated. Thank you.

Answer 1

For every natural number x there is an integer
smaller than x such that their product is positive.

With restricted quantifies.
For all natural nunber x, existx integer y with (y <`x and 0 < xy).

Without restricted quantifies.
For all x, (x natural number implies
exists y with (y integer and y < x and 0 < xy))