Exercise 2, § 3

If E and F are distinct sets, show that $\mathrm{E}^{\mathrm{F}} \neq \mathrm{F}^{\mathrm{E}}$. Deduce that if E and F are the cardinals 2 and $4(= 2 + 2)$, then at least one of the sets $\mathrm{E}^{\mathrm{F}}$, $\mathrm{F}^{\mathrm{E}}$ is not a cardinal.