Question

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? 

Answer 1

Let C denote the set of people who like cricket, and T denote the set of people who like tennis 

∴ n(C ∪ T) = 65, n(C) = 40, n(C ∩ T) = 10

 We know that:

 n(C ∪ T) = n(C) + n(T) – n(C ∩ T) 

∴ 65 = 40 + n(T) – 10

⇒ 65 = 30 + n(T) 

⇒ n(T) = 65 – 30 = 35 

Therefore, 35 people like tennis.

 Now,

 (T – C) ∪ (T ∩ C) = T

 Also, 

(T – C) ∩ (T ∩ C) = Φ 

∴ n (T) = n (T – C) + n (T ∩ C) 

⇒ 35 = n (T – C) + 10 

⇒ n (T – C) = 35 – 10 = 25 

Thus, 25 people like only tennis.