Cardinality of Set of All Mappings/Examples/2 Elements to 2 Elements

Example of Cardinality of Set of All Mappings
Let $X = \set {a, b}$.

Let $Y = \set {u, v}$.

Then the mappings from $X$ to $Y$ are:

$f_1$ and $f_4$ are bijections.

$f_2$ and $f_3$ are neither surjections nor injections.