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Chapter 13: Q 12. (page 847)

If $n (A) = 30, n (B) = 40, n (A \cup B) = 45$ , find $n (A \cap B)$ .

Short Answer

Expert verified

$n (A \cap B) = 25$ .

Step by step solution

01

Step 1. Given Information.

The given values are

$n (A) = 30, n (B) = 40, n (A \cup B) = 45$ .

02

Step 2. Value of nA∩B.

Using the Counting principle, we get

$\begin{array}{rcl} n (A \cup B) & = & n (A) + n (B) - n (A \cap B) \\ 45 & = & 30 + 40 - n (A \cap B) \\ 45 & = & 70 - n (A \cap B) \\ - 25 & = & - n (A \cap B) \\ n (A \cap B) & = & 25 \end{array}$ .

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