Exercise 7, § 6

Let E, F be two infinite sets such that Card (E) < Card (F). Show that the set of all subsets of F which are equipotent to E and the set of all injections of E into F are both equipotent to the set $F^E$ of all mappings of E into F (for each mapping $f$ of E into F, consider the injection $x \rightarrow (x, f(x))$ of E into $E \times F$).