In a survey it was found that 21 liked product A , 26 liked product b , and 29 liked product c , 14 liked products a and b , 12 liked products c and a , 14 liked products b and c and 8 liked all the three products , find how many liked products c only?
Answers
29 -12 – 14 + 8
11
Concept: A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different visually.
Given: No. of people liked product A = 21
No. of people liked product B = 26
No. of people liked product C = 29
No. of people liked product A and B = 14
No. of people liked product C and A = 12
No. of people liked product B and C = 14
No. of people liked product A, B and C = 8
To find: No. of people liked product C only
Solution:
As it is given that
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
Refer the Venn Diagram for clear explanation
from the venn diagram it is clear that, people who liked only product C are
29 - (4 + 8 + 6)
29 - 18
11
Hence, only 11 people liked product C only.
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