Question

If $G=\{7,8\}$ and $H=\{5,4,2\}$, find $G\times H$ and $H\times G$.

Answer 1

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

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