Question

Given $n(U)=20,n(A)=12,n(B)=9,$ $n(A\cap B)=4,$ where $U$ is the universal set, A and B are subsets of $U$ then $n[(A\cup B{)}^c]$ equals to:

• A. 17
• B. 9
• C. 11
• D. 3
• E. 16

Answer 1

Answer: (D)

$n(U)=20,n(A)=12,n(B)=9,n(A\cap B)=4$
$\therefore$ $n(A\cup B)=n(A)+n(B)-n(A\cap B)$ $=12+9-4=17$ Hence, $n[{(A\cup B)}^c]=n(U)-n(A\cup B)$
$=20-17=3$