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?

Asked by Abhisek | 2 years ago |  85

##### Solution :-

Consider C as the set of people who like cricket

T as the set of people who like tennis

n(C ∪ T) = 65

n(C) = 40

n(C ∩ T) = 10

It can be written as

n(C ∪ T) = n(C) + n(T) – n(C ∩ T)

Substituting the values

65 = 40 + n(T) – 10

By further calculation

65 = 30 + n(T)

So we get

n(T) = 65 – 30 = 35

Hence, 35 people like tennis.

We know that,

(T – C) ∪ (T ∩ C) = T

So we get,

(T – C) ∩ (T ∩ C) = Φ

Here

n (T) = n (T – C) + n (T ∩ C)

Substituting the values

35 = n (T – C) + 10

By further calculation

n (T – C) = 35 – 10 = 25

Therefore, 25 people like only tennis.

Answered by Pragya Singh | 2 years ago

### Related Questions

#### If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

#### Prove that A – B = A ∩ B.’

Prove that A – B = A ∩ B.’

#### Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.