Question

In a survey, 21 people liked product A, 26 liked product B and 29 liked product C. 14 people liked both A and B.  12 liked C and A.  14 liked B and C and 8 liked all the three products.  How many liked the product C only?

Answer 1

People like A=n(A)=21
People like B=n(B)=26
People like C=n(C)=29
People like both A and B=n(A{intersection}B)=14
People like both A and C=n(A{intersection}C)=12
People like both B and C=n(B{intersection}C)=14
People like  A,B and C=n(A{intersection}B{intersection}C)=8
people who like only C=n(C)-n(A{intersection}C)-n(B{intersection}C)+n(A{intersection}B{intersection}C=29-12-14+8=11

Answer 2

Answer:

Step-by-step explanation:

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.

"/" represents intersection.

Cap B means capital B or B set...alright

Thanks & Regards

Rate my ans and dont forget to thank me....☆☆☆☆☆