Question 7 - Number of elements in set - 2 sets - (Using properties) - Chapter 1 Class 11 Sets

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Question 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