Exercise 2, § 6

Show that, if $\mathfrak{a}, \mathfrak{b}, \mathfrak{c}, \mathfrak{d}$ are four cardinals such that $\mathfrak{a} < \mathfrak{c}$ and $\mathfrak{b} < \mathfrak{d}$, then $\mathfrak{a} + \mathfrak{b} < \mathfrak{c} + \mathfrak{d}$ and $\mathfrak{a}\mathfrak{b} < \mathfrak{c}\mathfrak{d}$ (cf. Exercise 21 (c)).