Question

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 people like both coffee and tea?

Answer 1

Let C is the set of people who like coffee.
T is the set of people who like tea.
Given,
Total number of people , n(T U C) = 70
number of people who like coffee , n(C) = 37
number of people who like tea , n(T) = 52

use formula,
n(T ∪ C) = n(T)+ n(C) - n(T ∩ C)

 70 = 52+37 - n(T ∩ C)

70 = 89 - n(T ∩ C)

n(T ∩ C) = 89-70

∴ n(T ∩ C) = 19

Thus, 19 people like both Tea and Coffee.

Answer 2

Answer:

n(C∩T) = 19

Step-by-step explanation:

Let number of people who likes coffee n(C) = 37,

number of people who likes Tea n(T) = 52 ,

Total number people in the group n(C∪T) = 70

Number people who like both

Coffee and Tea = n( C∩T ) = ?

We know that ,

n( C∩T ) = n(C) + n(T) - n( C∪T )

= 37 + 52 - 70

= 89 - 70

= 19

∴ Number people who like both

Coffee and Tea = 19

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