Question

"SETS"
1. in a group of 65 persons,20 drink tea but not coffee,38 drink tea and 15 take nither of the two find,
A. How many drink tea and coffee both.
B.How many drink coffee but not tea.​

Answer 1

Let U be the set of all persons, A be the set of those who drink coffee and B be the set of those who drink tea.

given,

n(U) = 65

n(B) = 38

n(B-A) = 20

n(AUB)' = 15

a) n(B) = n(B-A) + n(AΠB)

38 = 20 + n(AΠB)

38-20 = n(AΠB)

18 = n(AΠB)

Thus, 18 persons drink tea and coffee both...

b) n(AUB) = n(U) - n(AUB)'

= 65 - 15 = 50

now, n(AUB) = n(A-B) + n(B-A) + n(AΠB)

50 = n(A-B) + 20 + 18

50 = n(A-B) + 38

50 - 38 = n(A-B)

12 = n(A-B)

Thus, 12 persons drink coffee but not tea...