First slide

Operations on Sets

Question

$Given n (U) = 20, n (A) = 12, n (B) = 9, n (A \cap B) = 4, where U is the universal set, A and B are subsets of U, then$ $n ((A \cup B)^{C}) =$

Easy

A

17
B

9
C

11
D

3

Solution

$\begin{aligned} n (A \cup B) = n (A) + n (B) - n (A \cap B) = 12 + 9 - 4 = 17 \\ Now, n ((A \cup B)^{c}) = n (U) - n (A \cup B) = 20 - 17 = 3 \end{aligned}$

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