Question

In a survey it was found that 21 people 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 how many liked product C only. 

Answer 1

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                             

It can be seen that number of people who like product C only is 

{29 – (4 + 8 + 6)} = 11