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Thread: [SOLVED] one-to-one and onto functions

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    [SOLVED] one-to-one and onto functions

    Give an example of two finite sets A and B and two functions f:A goes to B and g:B goes to A, such that f is one-to-one but not onto and g is onto but not one-to-one.
    Maybe I'm over thinking this (or under thinking) but I can't seem to find a way that this is even possible. Help please!
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    Quote Originally Posted by deathbyproofs View Post
    Give an example of two finite sets A and B and two functions f:A goes to B and g:B goes to A, such that f is one-to-one but not onto and g is onto but not one-to-one.
    Maybe I'm over thinking this (or under thinking) but I can't seem to find a way that this is even possible. Help please!
    Should be easy. For example, take $\displaystyle A=\{0\}, B=\{0,1\}$ and define $\displaystyle f\colon A\to B$ and $\displaystyle g\colon B\to A$ as follows.

    $\displaystyle \begin{tabular}{c|c}
    $A$ & $0$\\\hline
    $f(A)$ & $0$
    \end{tabular}$

    $\displaystyle \begin{tabular}{c|cc}
    $B$ & $0$ & $1$\\\hline
    $g(B)$ & $0$ & $0$
    \end{tabular}$
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  3. #3
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    I can't believe I didn't see this to begin with I was really over thinking it! Thanks so much!
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