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Question:
Let $U$ be the universal set containing 700 elements. If $A, B$ are sub-sets of $U$ such that $n(A)=200, n(B)=300$ and $(A \cap B)=100$. Then $n\left(A^{\prime} \cap B^{\prime}\right)=$
(a) 400
(b) 600
(c) 300
(d) none of these.
Solution:
(c) 300
$n\left(A^{\prime} \cap B^{\prime}\right)=n(A \cup B)^{\prime}$
$=n(U)-n(A \cup B)$
$=700-\{200+300-100\}$
$=300$
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