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Misc 16 - 21 people liked product A, 26 liked B, 29 liked C

Misc 16 - Chapter 1 Class 11 Sets - Part 2
Misc 16 - Chapter 1 Class 11 Sets - Part 3 Misc 16 - Chapter 1 Class 11 Sets - Part 4


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Misc 16 In a survey it was found that 21 people liked product A, 26 liked product B & 29 liked product C. If 14 people liked products A & B, 12 people liked products C & A, 14 people liked products B & C and 8 liked all the three products. Find how many liked product C only. Let A, B, C be the set of people who like product A, product B & product C respectively Number of people who liked product A = n(A)= 21, Number of people who liked product B = n(B)= 26, Number of people who liked product C = n(C) = 29, Number of people who liked product A and B = n(A ∩ B) = 14, Number of people who liked product C and A = n(C ∩ A) = 12, Number of people who liked product B and C = n(B ∩ C) = 14, Number of people who liked all three products A ,B and C = n(A ∩ B ∩ C) = 8 We have to find how many people liked product C only. Let us draw a Venn diagram Let a denote number of people who liked product A & B but not C. Let b denote number of people who liked product A & C but not B. Let c denote number of people who liked product B & C but not A. Let d denote the number of people who liked all three products. Number of people who liked product C only = n(C) – b – d – c Now, d = n(A ∩ B ∩ C) = 8 Given n(A ∩ C) = 12 b + d = 12 Putting d = 8 b + 8 = 12 b = 12 – 8 b = 4 Similarly, n(B ∩ C) = 14 c + d = 14 Putting d = 8 c + 8 = 14 c = 14 – 8 c = 6 Number of people who liked product C only = n(C) – b – d – c = 29 – 4 – 8 – 6 = 11 Hence, number of people who like product C only is 11

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.