In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like both coffee and tea?

Asked by Sakshi | 1 year ago |  97

##### Solution :-

We have,

A total number of people = 70

Number of people who like Coffee = n (C) = 37

Number of people who like Tea = n (T) = 52

Total number = n (C ∪ T) = 70

Person who likes both would be n (C ∩ T)

We know,

n (C ∪ T) = n (C) + n (T) – n (C ∩ T)

Substituting the values we get

70 = 37 + 52 – n (C ∩ T)

70 = 89 – n (C ∩ T)

n (C ∩ T) =19

There are 19 persons who like both coffee and tea.

Answered by Aaryan | 1 year 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}.

#### Prove that A ∩ (A ⋃ B)’ = ϕ

Prove that A ∩ (A ⋃ B)’ = ϕ

#### If A = {3, {2}}, find P(A).

If A = {3, {2}}, find P(A).