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In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked 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 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.

Grade:Upto college level

3 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
Let A, B and C denote the set of people who like products A, B and C respectively.
Then it is given that 21 people like product A, i.e. n(A) = 21.
Similarly, we have n(B) = 26 and n(C) = 29.
Now, 14 people like both A and B, so this means n(A \cap B) = 14.
Similarly, n(C \cap A) = 12, n(B \cap C) = 14 and n(A \cap B \cap C) = 8.
The number of people who liked just product C is given by =
n(C) – n(C \cap A) – n(B \cap C) + n(A \cap B \cap C)
( you can also create venn diagram for the same, the formula will be clearer in that case)
= 29-12-14+8
= 11.
Hence,11 people liked only product C.
Thanks & Regards
Latika Leekha
askIITians Faculty
Vijay
13 Points
2 years ago
Let A, B, and C be the set of people who like product A, B, and C respectively. 
n(A) = 21, n(B) = 26, n(C) = 29, n(A ∩ B) = 14, n(C ∩ A) = 12, n(B ∩ C) = 14, n(A ∩ B ∩ C) = 8 
People who many liked product C only 
= n(C) - n(C ∩ A) - n(B ∩ C) + n(A ∩ B ∩ C) 
= 29 -12 – 14 + 8 
= 11 
Hence, 11 liked product C only
Yash Chourasiya
askIITians Faculty 256 Points
10 months ago
Dear Student

Let A, B, and C be the set of people who like product A, product B, and product C respectively.
Accordingly,
n(A) = 21, n(B) = 26, n(C) = 29
n(A ∩ B) = 14, n(C ∩ A) = 12, n(B ∩ C) = 14
n(A ∩ B ∩ C) = 8
The Venn diagram for the given problem can be drawn as
643-465_25.PNG
It can be seen that number of people who like product C only is { 29 – (4 + 8 + 6) } = 11

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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