Originally Posted by

**issacnewton** I just have some general question regarding functions. Consider the sets A and B. Now if $\displaystyle A\neq \varnothing\mbox{ and }B=\varnothing$, then the definition of the function$\displaystyle f:A\to B$ fails but there is still a function $\displaystyle g:B\to A$, even though in both cases $\displaystyle A\times B=\varnothing$ . So if we define $\displaystyle ^AB$ as the set of functions from A to B, then if $\displaystyle B=\varnothing\mbox{ and } A\neq \varnothing$, then

$\displaystyle ^AB=\varnothing\mbox{ and } ^BA=\{\varnothing\}$

is that right reasoning ? I need this result in some proof.