# In a group of 50

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.

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