For a homework assignment, I am asked to show that two sets A and B are equinumerous. I am wondering, if showing that the cardinality of A is equal to the cardinality of B, is enough to say a bijection exists which implies they are equinumerous? It is important to note that in the problems, the sets A and B are finite and countable. One of the problems is shown to give you a feel:
Prove that the following couples of sets are equinumerous by finding a one-to-one relation between them.
A is the fingers of one hand, B is the set of vowels
P.S. I don't want a solution, this is homework, I just want to know if I am on the right track on tackling the problem, thank you.