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.

• A. 10
• B. 11
• C. 12
• D. 13

Answer 1

The correct option is B 11

Let $A$, $B$, and $C$ be the set of people who like $productA$, $productB,andproductC$ respectively.

Accordingly,

$n\left(A\right)=21,n\left(B\right)=26,n\left(C\right)=29,n(A\cap B)=14,n(C\cap A)=12$,

$n(B\cap C)=14,n(A\cap B\cap C)=8$

The Venn diagram for the given problem can be drawn as above.

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

$=29–(4+8+6)=11$