Show that the function \( f: \mathbf{N} \rightarrow \mathbf{N} \) defined by\[f(n)=\left\{\begin...

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Show that the function \( f: \mathbf{N} \rightarrow \mathbf{N} \) defined by\[f(n)=\left\{\begin{array}{c}n+1, \text { if } n \text { is odd } \\n-1, \text { if } n \text { is even }\end{array}\right.\]is both one-one and onto.
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