#### 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?

#### Solution

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.

Is there an error in this question or solution?

Solution 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? Concept: Practical Problems on Union and Intersection of Two Sets.