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Ex 1.6, 7 - In a group of 65 people, 40 like cricket, 10 both

Ex 1.6, 7 - Chapter 1 Class 11 Sets - Part 2
Ex 1.6, 7 - Chapter 1 Class 11 Sets - Part 3

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Ex 1.6, 7 In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis? Let C & T denote the set of people who like cricket & tennis resp. Number of people in the group = Number of people who like cricket or tennis = n(C ∪ T) = 65, Number of people who like cricket = n(C) = 40, Number of people who like both cricket and tennis = n(C ∩ T) = 10 We know that n(C ∪ T) = n(C) + n(T) – n(C ∩ T) 65 = 40 + n(T) – 10 65 = 40 – 10 + n(T) 65 = 30 + n(T) 65 – 30 = n(T) 35 = n (T) n(T) = 35 Therefore, 35 people like tennis. Number of people who like only tennis but not cricket Number of people who like only tennis but not cricket = Number of people who like tennis – Number of people who like both tennis and cricket = n(T – C) = n(T) – n(T ∩ C) = 35 – 10 = 25 Thus, 25 people like only tennis. People who like only tennis People who like both tennis & cricket

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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.