Question

In a group of 70 people ,37 like coffee,52 like tea,each of them like atleast one of the two drinks.how many people like both coffee and tea

Answer 1

19 People

Let C be the set of the people who like coffee.

Let T be the set of the people who like tea.

n(C) = 37

n(T) = 52

n(C U T) = 70

To Find:

n(C ⋂ T) = ?

Calculating:

The formula that we use to calculate the union of sets is:

n(C U T) = n(C) + n(T) - n(C ⋂ T)

Taking n(C ⋂ T) to the other side of the formula we get:

n(C ⋂ T) = n(C) + n(T) - n(C U T)

Substituting all the values that are known to us into this formula we get:

n(C ⋂ T) = 37 + 52 - 70

n(C ⋂ T) = 89 - 70

n(C ⋂ T) = 19

Therefore, 19 People like both coffee and tea.