Let \(n(U) = 700 , n(A) = 200 , n(B) = 300,
n(A∩B)=100, then n(A' ∩ B')=

400

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600

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500

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300

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Solution

The correct option is D $300$
By De Morgan's Second Law, we have
$n (A^{'} \cap B^{'}) = n (A U B)^{'}$
$n (A^{'} \cap B^{'}) = n (U) - n (A U B)$
$n (A^{'} \cap B^{'}) = n (U) - (n (A) + n (B)) - n (A \cap B))$
$n (A^{'} \cap B^{'}) = 700 - (200 + 300 - 100)$
$n (A^{'} \cap B^{'}) = 300$

$n (A' \cap B') = n (A \cup B)' = n (U) - n (A \cup B) = n (U) - (n (A) + n (B) - n (A \cap B)) = 700 - (200 + 300 - 100) \Rightarrow n (A' \cap B') = 300$

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