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:
Given
n(A) = 21
n(B) = 26
n(C) = 29
n(A∩B) = 14
n(B∩C) = 14
n(A∩C) = 12
And n(A∩B∩C) = 8
Now people who like only product C is
n(C) - n(A∩C) - n(B∩C) + n(A∩B∩C)
= 29 -12 - 14 + 8
= 37 - 26
= 11
So people who like only product C is 11.
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