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 = set of people who like cricket 

T = set of people who like tennis. 

Then n(C ∪ T) = 65; n(C) = 40; n(C ∩ T) = 10

∴ n(T) = n{C∪T) + n(C∩T)-n(C)

= 65 + 10-40 = 35

Number of people who like tennis only

n(T-C) = n(T)-n(C ∩ T)

= 35-10 = 25