Bijection/Examples/Arbitrary Mapping on Sets

Example of Bijection

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

Let $B = \set {b_1, b_2, b_3, b_4}$.

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

$f = \set {\tuple {a_1, b_3}, \tuple {a_2, b_2}, \tuple {a_3, b_4}, \tuple {a_4, b_1} }$

Then $f$ is a bijection.