Question

in a survey of group people showed that 60 liked tea, 45 liked coffee, 30 liked milk,25 liked coffee as well as tea,20 liked tea as well as milk,15 liked coffee as well as milk and 10 liked all the three. How many people were asked this question?​

Answer 1

85 people were surveyed

Explanation:

Let n(X0 represent the number of people who belong in set X

We have 3 sets here
T = set of all people who like tea

C = set of all people who like coffee

M = set of all people who like milk

From the info given

n(T) = 60
n(C) = 45

n(M) = 30

The intersection of the sets are
n(C ∩ T) = 25

n(T ∩ M) = 20

n(C ∩ M) = 15

n(C ∩ T ∩ M) = 10

The number of people who were asked this question is given by

n(T U C U M)

= n(T) + n(C) + n(M) - n(C ∩ T) - n(T ∩ M) - n(C ∩ M) + n(C ∩ T ∩ M)

= 60 + 45 + 30 - 25 - 20 - 15 + 10

= 85

Venn Diagram is attached

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