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Question

In a group of 65 people 40 like cricket, 10 like both cricket and tennis, how like tennis only and not cricket?


Solution

Let C and T represent the set people who like cricket and tennis respectively. 
Number of people like cricket or tennis, n(C ∪ T) = 65. 
Number of people likes tennis, n(C) = 40. 
Number of people likes both cricket and tennis, n(C ∩ T) = 10 
Use the formula 
n(C ∪ T) = n(C) + n(T) - n(C ∩ T) 
⇒ 65 = 40 + n(T) - 10 
⇒ 65 = 30 + n(T) 
⇒ 65 - 30 = n(T) 
⇒ 35 = n(T) 
Hence, 35 people like tennis. 
Number of people How many like tennis only and not cricket,
⇒  n(T - C) = n(T) – n(T ∩ C) ⇒ 35 -10 ⇒  25. 
Thus, 25 people like only tennis. 

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