- (i)
- is an injection;
- (ii)
- is a surjection;
- (iii)
- is a bijection.

- Suppose that is an injection. Then the set is finite and . It follows that is a subset of such that , hence , i.e. is a surjection.
- Suppose that is a surjection, i.e. . Thus and must be an injection.

and |

Then is surjective but not injective and is injective but not surjective.

- If we wish to place 8 books on a shelf, there are possible orderings. .
- We wish to place 5 chemistry books and 8 physics books on the same shelf, letting together books of the same discipline. Among the chemistry books, there are orderings and among the physics books, there are orderings. Axs there are two choices for the respective places of the discipline (physics on the left and chemistry on the right, or physics on the right and chemistry on the left), the number of different orderings is here .