Question

1. a magazine poll sampling 90 people gives the following results: 17 read magazine a, 18 read magazine b, 14 read magazine c, 8 read magazine a and b, 7 read magazine a and c, 9 read magazine b and c, 5 read all three magazines

Explanation:

Step1: Recall the principle of inclusion - exclusion

The formula for \(|A\cup B\cup C|\) is \(|A|+|B|+|C|-|A\cap B|-|A\cap C|-|B\cap C|+|A\cap B\cap C|\).
Let \(|A| = 17\), \(|B| = 18\), \(|C| = 14\), \(|A\cap B| = 8\), \(|A\cap C| = 7\), \(|B\cap C| = 9\), and \(|A\cap B\cap C| = 5\).

Step2: Substitute the values into the formula

\[

$$\begin{align*} |A\cup B\cup C|&=17 + 18+14-8 - 7-9 + 5\\ &=(17 + 18+14)+5-(8 + 7+9)\\ &=49 + 5-24\\ &=30 \end{align*}$$

\]

Answer:

30