Let `f: Nuu{0}->Nuu{0}` be defined by `f(n)={n+1,\ if\ n\ i s\ even nn-1,\ if\ n\ i s\ od d` Show that `f` is a bijection.

Explanation

Given,.`f(n)={n−1,n=`odd and `n+1,n=`even}

When n is odd

`f(n_1​)=f(n_2​)`

`=>n_1​−1=n_2​−1`

`=>n_1​=n_2​`

When n is even

`f(n_1​)=f(n_2​)`

`=>n_1​+1=n_2​+1`

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