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Chapter 13: Q 14. (page 847)

If $n (A \cap B) = 40, n (B) = n (A), n (A \cup B) = 60$ . Find $n (A)$ .

Short Answer

Expert verified

$n (A) = 50$ .

Step by step solution

Step 1. Given Information.

The given values are

$n (A \cap B) = 40, n (B) = n (A), n (A \cup B) = 60$ .

Step 2. Calculation of nA.

Using the Counting principle, we get

$\begin{array}{rcl} n (A \cup B) & = & n (A) + n (B) - n (A \cap B) \\ 60 & = & 2 n (A) - 40 \\ 100 & = & 2 n (A) \\ n (A) & = & 50 \end{array}$ .

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IfnA∩B=40,nB=nA,nA∪B=60. FindnA.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation of nA.

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If $n (A \cap B) = 40, n (B) = n (A), n (A \cup B) = 60$ . Find $n (A)$ .