Mathematics > sets-relations-and-functions > Relations And Functions

Show that the function $f: N \rightarrow N$, where $N$ is a set of natural numbers, given by $f(n) = \begin{cases} n - 1, & \text{if } n \text{ is even} \\ n + 1, & \text{if } n \text{ is odd} \end{cases}$ is a bijection.