Question

In a survey i was found that 21 persons liked product $P_1$, 26 liked product $P_2$ and 29 liked product $P_3$. If 14 persons liked products $P_{1}and{P}_2$ ; 12, persons liked prooduct $P_3$ and $P_1$; 14 persons liked products $P_2$ and $P_3$ and 8 liked all the three products. Find how many liked product $P_3$ only.

Answer 1

Let $n\left(P_1\right)$ be the number of persons liking product $P_1$

$n\left(P_2\right)$ be the number of persons liking product $P_2$

and $n\left(P_3\right)$ be the number of persons liking product $P_3$

Then, $n\left(P_1\right)=21,n\left(P_2\right)=26,n\left(P_3\right)=29,n(P_1\cap P_2)=14$,

$n(P_1\cap P_3)=12,n(P_2\cap P_3)=14,n(P_1\cap P_2\cap P_3)=8$

$\therefore$ Number of people liking product $P_3$ only

= 29- (4+8+6)

= 29-18

= 11

Hence, 11 persons liked product $P_3$ only.