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 $n (A^{'} \cap B^{'}) =$

90

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40

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10

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20

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Solution

The correct option is C $10$
$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$= 50 + 60 - 20 = 90$
$Now, n (A^{'} \cap B^{'}) = n (A \cup B)^{'}$
$= n (U) - n (A \cup B)$
$= 100 - 90 = 10$

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