Question

If $n(A)=10,n(A\cap B)=4$, then how many elements are in $(A\cap B{)}^{\prime }\cap A$

Answer 1

Answer: 6

$n(A\cap B{)}^{\prime }\cap A=n{A}^{\prime }\cup B^{\prime }\cap A$
$=n{A}^{\prime }\cap A\cup B^{\prime }\cap A$
$=n{B}^{\prime }\cap A$
$=n(A)-n(A\cap B)$
$\Rightarrow n(A\cap B{)}^{\prime }\cap A=10-4=6$