/sci/ - Science & Math

What is a function i can define for any two sets?

I am trying to prove that
[math]X^{Y} = Y^{X} \Leftrightarrow X = Y [/math]

I need to define a function from X to Y so i can say [math]Y^{X}[/math] is not empty. I was thinking of the constant function, like f(x) = a. But a has to exist in Y first so I don't know how to proceed. Is there another function that guarantees Y is not empty or something?