Exercise 27.

Let \(f:X \to Y\) be a function and \(B \subseteq Y\) be a finite subset of the codomain. What can you say about the relationship between \(\card{B}\) and \(\card{f\inv(B)}\text{?}\) Consider both the general case and what happens when you know \(f\) is injective, surjective, or bijective.

Solution.
in-context