Question

Let $A$$=\{1,2\},$ and $B$$=\{1,3\},$ then prove that $(A\times B)\cup (B\times A)=\left\{\right(1,3),(2,3),(3,1),(3,2),(1,1),(1,2),(2,1\left)\right\}$

Answer 1

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

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

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

$(A\times B)\cup (B\times A)$

$\Rightarrow \left\{\right(1,1\left)\right(1,3\left)\right(2,1\left)\right(2,3\left)\right(1,2\left)\right(3,1\left)\right(3,2\left)\right\}$