First slide

Operations on Sets

Question

Let X be the universal set for sets A and B. If $n (A) = 200, n (B) = 300 and n (A \cap B) = 100$ , then $n (A^{'} \cap B^{'})$ is equal to 300 provided n(X) is equal to

Easy

A

600
B

700
C

800
D

900

Solution

Given $n (A) = 200, n (B) = 300 and n (A \cap B) = 100$
we know that
$\begin{array}{l} n (A \cup B) = n (A) + n (B) - n (A \cap B) \\ n (A \cup B) = 200 + 300 - 100 = 400 \\ Also, n (A^{'} \cap B^{'}) = n \{(A \cup B)^{'}\} \\ = n (X) - n (A \cup B) \\ \Rightarrow 300 = n (X) - 400 \\ \Rightarrow n (X) = 700 \end{array}$

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