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  4. 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 ∩B) = 20 then n (A' ∩ B') =

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Q. 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') =

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Solution:

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