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 denote the set of people who like cricket and T denote the set of people who like tennis. Then C ∪ T is the set of people who like at least one of the two games and C ∩ T is the set of people who like both cricket and tennis.
Then n(C) = 40, n(C ∪ T) = 65 and n(C ∩ T) = 10

Method 1:
We know,
n(C ∪ T) = n(C) + n(T) - n(C ∩ T)
65 = 40 + n(T) - 10
n(T) = 65 - 40 + 10 
.^..  n(T) = 35
Therefore, number of people who like tennis = n(T) = 35 
and the number people who like only tennis and not cricket = n(T) - n(C ∩ T) = 35 - 10 = 25