Question

In a survey it was found that 21 persons 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: 

(a) the number of people who liked at least one product 

(b) the number of people who liked product C only

Answer 1

Given 

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 

(a)  n(A ∪ B ∪ C) = n(A) + n(B) + N(C) − n(A ∩ B) 

n(B ∩ C) − n(C ∩ A) + n(A ∩ B ∩ C) 

= 21 + 26 + 29 – 14 – 12 – 14 + 8 

(b)  n(C only) = n(C) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C) 

= 29 – 12 – 14 + 18 

= 11