Question

If U is the universal set with 100 element; A and B are two set such that n(A) = 50, n (B) = 60, n (A $\cap$B) = 20 then n (A' $\cap$ B') =

• A. 90
• B. 40
• C. 10
• D. 20

Answer 1

Answer: (C)

$n\left(U\right)=100$
$n\left(A\right)=50$
$n\left(B\right)=60$
$n\left(A\cap B\right)=20$
$n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)$
$=50+60-20$
$=110-20$
$=90$
$n\left(A^{\prime }\cap B^{\prime }\right)=n\left({\left(A\cup B\right)}^{\prime }\right)$
$=n\left(U\right)-n\left(A\cup B\right)$
$=100-90$
$=10$