Inverse Mapping/Examples/Arbitrary Finite Set with Itself

Example of Compositions of Mappings
Let $X = Y = \set {a, b}$.

Consider the mappings from $X$ to $Y$:

We have that:
 * $f_1$ is the inverse mapping of itself
 * $f_4$ is the inverse mapping of itself


 * the inverse of neither $f_2$ nor $f_3$ are mappings.