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A function $\mathrm{f}$ from the set of natural numbers to integers defined by $\mathrm{f}(\mathrm{n})=\left\{\begin{array}{l}\frac{\mathrm{n}-1}{2} \text {, when } n \text { isodd } \\ \frac{\mathrm{n}}{2} \text {, when } \mathrm{n} \text { is even }\end{array}\right.$ is
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one-one and onto both.
one-one and onto both.
$f: N \rightarrow 1$
$f(1)=0, f(2)=-1, f(3)=-1, f(4)=-2$
$f(5)=2$, and $f(6)=-3$ so on.
In this type of function every element of set $\mathrm{A}$ has unique image in set $\mathrm{B}$ and there is no element left in set $\mathrm{B}$. Hence $\mathrm{f}$ is one-one and onto function.
$f(1)=0, f(2)=-1, f(3)=-1, f(4)=-2$
$f(5)=2$, and $f(6)=-3$ so on.
In this type of function every element of set $\mathrm{A}$ has unique image in set $\mathrm{B}$ and there is no element left in set $\mathrm{B}$. Hence $\mathrm{f}$ is one-one and onto function.
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