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

Make the Venn diagram for the above given and from there we can get an idea of overall distribution of number of people liking one or two or all three sets and hence once getting the idea of overall distribution we can get an idea and from there we can calculate the number of people who likes C product only.

Complete step by step solution:
As given,
21 people likes A,
26 people likes B,
29 people likes C,
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.
Now, we have to find people who like only product C and hence making Venn Diagram as,

Let the number of people who likes only product C be x
Always start filling the set from the intersection of all three sets and then move further elements of intersection of two sets and then finally proceed to fill the number of elements in particular sets.
As we know that total numbers of elements in set C is 29
Hence, forming the equation with the help of Venn Diagram as,
$\Rightarrow 4 + 6 + 8 + x = 29$
On solving above equation,
$\Rightarrow x = 29 - 18$
On subtraction, we get,
$\Rightarrow x = 11$

Hence the number of people who like only product C is 11.

Note:
A Venn diagram, also called primary diagram, set diagram or logic diagram, is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves.
A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. The points inside a curve labelled S represent elements of the set S, while points outside the boundary represent elements not in the set S.