asked by XxBRAINLIANxX, 10 days ago

# 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.​

9

Number of peoples ho like C only.

For only C

n(C)−n(C∩A)−n(N∩C)+n(A∩B∩C)

⇒29{12+14}+8

⇒29−26+8

⇒11

8

Let us assume that,

U = the set of all students in the group

E = the set of students who know English

H = the set of the students who know Hindi

∴ H ∪ E = U

Number of students who know Hindi n (H) = 100

Number of students who knew English, n (E) = 50

Number of students who know both, n (H ∩ E) = 25

We have to find the total number of students in the group i.e. n (U)

∴ According to the question,

n (U) = n(H) + n(E) – n(H ∩ E)

= 100 + 50 – 25

= 125

∴ Total number of students in the group = 125 students

★ Number of students who only like product C

= {29 – (4 + 8 + 6)}

= {29 – 18}

= 11 students

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