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!

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.