Algebra> In a survey it was found that 21 people l...

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.

Manvendra Singh chahar , 12 Years ago

Grade Upto college level

3 Answers

Latika Leekha

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

Last Activity: 11 Years ago

Vijay

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

Last Activity: 7 Years ago

Yash Chourasiya

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

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

Last Activity: 5 Years ago