First slide

Operations on Sets

Question

$In a town of 10, 000 families it was$ $found that 40 % family buy$ $newspaper A, 20 % buy newspaper$ $B and 10 % families buy newspaper$ $C, 5 % families buy A and B, 3 % buy$ $B and C and 4 % buy A and C . If 2 %$ $families buy all the three$ $newspapers, then number of$ $families which buy A only is$

Moderate

A

3100
B

3300
C

2900
D

1400

Solution

$\begin{array}{l} n (A) = 40 %, n (A \cap B) = 5 %, n (A \cap C) = 4 %, n (A \cap B \cap C) = 2 % \\ n (A only) = n (A) - n (A \cap B) - n (A \cap C) + (A \cap B \cap C) \\ = 40 - 5 - 4 - 2 \\ = 33 % of 10000 \\ =3300 \end{array}$

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