I apologize in advance if this question is too basic to warrant a post. I just ran into the following question:
Let $f: A \to B$. If $A$ and $B$ are finite sets with the same number of elements, then $f: A \to B$ is bijective if and only if $f$ is injective if and only if $f$ is surjective.
The use of two "if and only if" statements has confused me; I am not exactly sure what I am trying to prove. I understand the function concepts being presented in the question, but I'm just not sure what I need to show. Therefore, I ask not for hints toward the solution of the question, but only the meaning of the question.