Question

If $A =\left\{1, 2 ,3\right\}, B=\left\{4, 5 , 6\right\}$ and $C =\left\{1, 2\right\}$ then the number of elements in the set $\left(A -B\right) \times\left(A\cap C\right)$ is

Answer 1

$A-B =\left\{1, 2, 3\right\}-\left\{4, 5, 6\right\}=\left\{1, 2, 3\right\}$
$A\cap C =\left\{1, 2, 3\right\}\cap\left\{1, 2\right\}=\left\{1, 2\right\}$
$\therefore \left(A -B\right)\times\left(A\cap C\right) = \left\{1, 2, 3\right\}\times\left\{1, 2\right\}$
$= \left\{\left(1, 1\right),\left(1, 2\right),\left(2,1\right),\left(2, 2\right),\left(3,1\right),\left(3,2\right)\right\}$