Let total number of people n(P) = 50
A number of people who drink Tea n(T) = 30.
A number of people who drink coffee n(C).
n(T–C) = 14
i. how may drink tea and coffee both.
We can see that T is disjoint union of n(T–C) and n (T ∩ C).
(If A and B are disjoint then n (A ∪ B) = n(A) + n(B))
∴ T = n(T–C) ∪ n (T ∩ C).
⇒ n(T) = n(T–C) + n (T ∩ C).
⇒ 30 = 14 + n (T ∩ C).
⇒ n(T ∩ C) = 16.
16 People drink both coffee and tea.
ii. how many drink coffee but not tea.
We know
n (P) = n(T) + n(C) – n (T ∩ C)
Substituting the values we get
50 = 30+n(C) – 16
n(C) = 36.
We can see that T is disjoint union of n(C–T) and n (T ∩ C).
(If A and B are disjoint then n (A ∪ B) = n(A) + n(B))
∴ C = n(C–T) ∪ n (T ∩ C).
⇒ n(C) = n(C–T) + n (T ∩ C).
⇒ 36 = n(C–T) + 16.
⇒ n(C–T) = 20.
20 People drink coffee but not tea.
