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A function \( f \) from the set of natural numbers to the set of integers defined by
\[
f(n)=\left\{\begin{array}{l}
\frac{n-1}{2}, \text { when } n \text { is odd } \\
-\frac{n}{2}, \text { when } n \text { is even }
\end{array}\right.
\]
(a) neither one-one nor onto
(b) one-one but not onto
(c) onto but not one-one
(d) one-one and onto both
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