Question

If $A=\{a,b\}$ and $B=\{1,2,3\}$ find $(A\times B)\cap (B\times A)$

Answer 1

We have $A=\{a,b\}$ and $B=\{1,2,3\}$

$A\times B=\{(a,1),(a,2),(a,3),(b,1),(b,2),(b,3)\}$

$B\times A=\{(1,a),(1,b),(2,a),(2,b),(3,a),(3,b)\}$

$(A\times B)\cap (B\times A)$

$=\{(a,1),(a,2),(a,3),(b,1),(b,2),(b,3)\}\cap \{(1,a),(1,b),(2,a),(2,b),(3,a),(3,b)\}=\varphi$