If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

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

$\mathrm{P} \times \mathrm{Q}=\{(p, q): p \in \mathrm{P}, q \in \mathrm{Q}\}$

$\therefore G \times H=\{(7,5),(7,4),(7,2),(8,5),(8,4),(8,2)\}$

$H \times G=\{(5,7),(5,8),(4,7),(4,8),(2,7),(2,8)\}$

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