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