Question

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

(i) product C only

(ii) product A and C but not product B

(iii) at least one of three products. like ​

Answer 1

Answer:11

Step-by-step explanation:

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.

Answer 2

Answer:

(i)11 (ii) 4 (iii)44

1. Step-by-step explanation:

(i) n(A)=21, n(B)=26,n(C)=29,n(A ∩ B)=14,n(B ∩ C)=14,(A∩ C)=12,n(A ∩B ∩ C)=8

n(only C)=n(C) -n(A ∩ C)-n(B ∩C) +n(A ∩ B ∩C)

              =29-12-14+8

              =11

(ii) n( A and C but not B)=n(A ∩ C)-(A ∩ B ∩ C)

                                      =12-8

                                      =4

(iii)n(A∩B∩C) =n(A)+n(B)+n(C)-n(A∩B) -n(B∩C)-n(A∩C)+n(A∩B∩C)

                     =21+26+29-14-14-12+8

•                      =44