Exercise 6, § 6

Let E, F be two infinite sets such that Card (E) $\leqslant$ Card (F). Show that (i) the set of all mappings of E onto F, (ii) the set of all mappings of E into F, and (iii) the set of all mappings of subsets of E into F are all equipotent to $\mathfrak{P}(F)$.