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In a survey it was found that 21 people liked prodúct A, 26 liked product B and29 liked product C. If 14 people liked products A and B, 12 people liked productsC 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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Answer» Let A, B and C denote the set of people who like products A, B and C respectively.Then it is given that 21 people like product A, i.e. n(A) = 21.Similarly, we have n(B) = 26 and n(C) = 29.Now, 14 people like both A and B, so this means n(A \cap B) = 14.Similarly, n(C \cap A) = 12, n(B \cap C) = 14 and n(A \cap B \cap C) = 8.The number of people who liked just product C is given by =n(C) – n(C \cap A) – n(B \cap C) + n(A \cap B \cap C)( you can also create venn diagram for the same, the formula will be clearer in that case)= 29-12-14+8= 11.Hence,11 people liked only product C. thnk uhh |
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