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Ex 1.6, 6 - In 70 people, 37 like coffee, 52 like tea - Ex 1.6

Ex 1.6, 6 - Chapter 1 Class 11 Sets - Part 2

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Ex 1.6, 6 In a group of 70 people, 37 like coffee, 52 like tea, and each person likes at least one of the two drinks. How many people like both coffee and tea? Let C denote the set of people who like coffee, and T denote the set of people who like tea Number of people who like coffee = n(C) = 37 Number of people who like tea= n(T) = 52 Number of people who like at least tea or coffee = n(C ∪ T) = 70 Number of people who like both tea & coffee = n(C ∩ T ) = ? We know that n(C ∪ T) = n(C) + n(T) – n(C ∩ T) 70 = 37 + 52 – n(C ∩ T) 70 = 89 – n(C ∩ T) n(C ∩ T) = 89 – 70 n(C ∩ T) = 19 Thus, 19 people like both coffee and tea.

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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.