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Ex 1.6, 7 - In a group of 65 people, 40 like cricket, 10 both - Number of elements in set  - 2 sets - (Using properties)

  1. Chapter 1 Class 11 Sets
  2. Serial order wise
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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 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.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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