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?

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
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.