Question:
If $\mathrm{G}=\{7,8\}$ and $\mathrm{H}=\{5,4,2\}$, find $\mathrm{G} \times \mathrm{H}$ and $\mathrm{H} \times \mathrm{G}$.
Solution:
$\mathrm{G}=\{7,8\}$ and $\mathrm{H}=\{5,4,2\}$
We know that the Cartesian product P × Q of two non-empty sets P and Q is defined as
$\mathrm{P} \times \mathrm{Q}=\{(p, q): p \in \mathrm{P}, q \in \mathrm{Q}\}$
$\therefore G \times H=\{(7,5),(7,4),(7,2),(8,5),(8,4),(8,2)\}$
$H \times G=\{(5,7),(5,8),(4,7),(4,8),(2,7),(2,8)\}$