Question

If $A=\{0,1\}$ and $B=\{1,2,3\}$, show that $A\times B\ne B\times A$

Answer 1

$A=\{0,1\}$

$B=\{1,2,3\}$

$A\times B=\left\{\right(0,1),(0,2),(0,3),(1,1),(1,2),(1,3\left)\right\}$

$B\times A=\left\{\right(1,0),(2,0),(3,0),(1,1),(2,1),(3,1\left)\right\}$

By the definition of equality of ordered pairs, the pair $(0,1)$ in $A\times B$ is not equal to the pair $(1,0)$ in $B\times A$

Therefore, $A\times B\ne B\times A$