In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only

Solution:

Let A be the set of people who liked product A.

B be the set of people who liked product B.

C be the set of people who liked product C.

It is given that

n (A) = 21, n (B) = 26, n (C) = 29, n (A ∩ B) = 14, n (A ∩ C) = 12, n (B ∩ C) = 14, n (A ∩ B ∩ C) = 8

Let’s draw the Venn diagram for the given problem

We can see that

Number of people who like product C only

= n (C) - (4 + 8 + 6)

= 29 - 18

= 11

Hence, 11 students liked product C only

NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 16

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

Summary:

In a survey, it was found that 21 people liked product A, 26 liked product B, and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products is given. We have found that 11 liked product C only