# [SOLVED] one-to-one and onto functions

• Feb 20th 2009, 06:33 PM
deathbyproofs
[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!
• Feb 20th 2009, 07:56 PM
Reckoner
Quote:

Originally Posted by deathbyproofs
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}$
• Feb 21st 2009, 06:57 AM
deathbyproofs
I can't believe I didn't see this to begin with I was really over thinking it! Thanks so much!