Question

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

Answer 1

Given: $G=\{7,8\}$ and $H=\{5,4,2\}$

Cartesian product of two sets
The cartesion product of two non-empty sets $P$ and $Q$ is
given as $P\times Q=\left\{\right(p,q):p\in P,q\in Q\}$
So, $G\times H=\left\{\right(7,5),(7,4),(7,2),(8,5),(8,4),(8,2\left)\right\}$
And $H\times G=\left\{\right(5,7),(4,7),(2,7),(5,8),(4,8),(2,8\left)\right\}$.