"Find two non-empty sets $A$ and $B$ for which $A^B$ and $B^A$ are not the same size."

I'm really not sure what this means or how to even go about attempting this... Can anyone provide an example of what it means for a set to be raised to an exponent of this sort?


$S^T$ is the set of all functions with domain $T$ and codomain $S$.

The reason for the notation is $$\left \vert {S^T}\right \vert = |S|^{|T|}$$

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    $\begingroup$ @Natalie: And you can demonstrate the difference by choosing $A$ and $B$ small enough that you can actually list all members of both $A^B$ and $B^A$, for concreteness. $\endgroup$ – MPW May 20 '15 at 3:27

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