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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.
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Solution
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
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