Let U be the universal set containing 700 elements.
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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