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.
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’s say A, B and C are the set of people who like product A, product B and product C respectively.

So now, as per the question,

n (A) = 21 be Number of students who like product A,

n (B) = 26 be Number of students who like product B,

n (C) = 29 be Number of students who like product C,

n(A \cap B)=14 be Number of students who like both products A and B,

n(C \cap A)=12 be Number of students who like both products A and C,

\mathrm{C} and \mathrm{B}, \mathrm{n}(\mathrm{B} \cap \mathrm{C})=14 be Number of students who like both product

n(A \cap B \cap C)=8 be Number of students who like all three product,

NCERT Solutions for Class 11 Chapter 1 Miscallenous Ex Image 2

Now from the Venn diagram, we have,

C=\{29-(4+8+6)\} be Number of students who only like product

=\{29-18\}

=11 students