Consider the following four sets of maps f : ℤ → ℚ:

I. {f : ℤ → ℚ : f is bijective and increasing}

II. {f : ℤ → ℚ : f is onto and increasing}

III. {f : ℤ → ℚ : f is bijective and satisfies that ∀ n ≤ 0, f(n) ≥ 0}, and

IV. {f : ℤ → ℚ : f is onto and decreasing}.

How many of these sets are empty?