Question

If A = {1, 2} and B = {1, 3} prove that $(A\times B)\cup (B\times A)$ = {(1, 3), (2, 3), (3, 1), (3, 2), (1, 1), (1, 2), (2, 1)}

Answer 1

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

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

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

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