Check if this function is surjective

Question

A function is defined by this formula: $$f: \mathcal P(\mathbb N) \times \mathcal P(\mathbb N) \to \mathcal P(\mathbb N) \times \mathcal P(\mathbb N) \\ f(x,y) = (x \setminus y, y\setminus x)$$

Is it enough to say that this function is not surjective because it will never take this value: $$(\mathbb N, \mathbb N)$$ or is it not "allowed"?

Answer 1

Yep, it's correct. Thats because $\mathbb N \subseteq \mathbb N$