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

#### 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!

#### Reckoner

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.

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

$$\displaystyle \begin{tabular}{c|cc} B & 0 & 1\\\hline g(B) & 0 & 0 \end{tabular}$$

• deathbyproofs

#### deathbyproofs

I can't believe I didn't see this to begin with I was really over thinking it! Thanks so much!