Permutation/Examples/Arbitrary Permutation on Sets

Example of Permutation
Let $A = \set {a_1, a_2, a_3, a_4}$.

Let $f \subseteq {A \times B}$ be the mapping defined as:


 * $f = \set {\tuple {a_1, a_3}, \tuple {a_2, a_4}, \tuple {a_3, a_1}, \tuple {a_4, a_2} }$

Then $f$ is a permutation on $A$.