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

Answer: 6

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