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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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Given n(A) = 21, n(B) = 26, n(C) = 29 

n(A∩B) = 14, n(A∩C) = 12, n(B∩C) = 14 

n(A∩B∩C) = 8

From the figure, number of persons liking product C 

only = n(C) – n(A∩C) – n(B∩C) + n(A∩B∩C)

= 29 - 12 - 14 + 8 = 11.

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