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.

Let us first assume A, B and C be the set of people who like product A, product B and product C respectively


Now, it is given in the question that:


Number of students who like product A, n (A) = 21


Number of students who like product B, n (B) = 26


Number of students who like product A, n (C) = 29


Number of students who like both product A and B,


Number of students who like both product A and B,


Number of students who like both product A and B,


Number of students who like all three product,


On the basis of given condition the venn diagram for the following question can be drawn as follows:



From the venn diagram, it can clearly be seen that:


Number of students who only like product C = {29 – (4 + 8 + 6)}


= {29 – 18}


= 11 students


16