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  4. If A and B are subsets of universal set U such that n(U) = 800, n(A) = 300, n(B) = 400 and n(A ∩ B) = 100. The number of elements in the set Ac ∩ Bc is

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Q. If $A$ and $B$ are subsets of universal set $U$ such that $n(U) = 800$, $n(A) = 300$, $n(B) = 400$ and $n(A \cap B) = 100$. The number of elements in the set $A^c \cap B^c$ is

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Solution:

$n(A \cup B) = n(A) + n(B) - n(A \cap B)$
$= 300 + 400- 100 = 600$
$n(A \cup B)^c = n(U) - n(A \cup B) = 800 - 600 = 200$