First slide

Operations on Sets

Question

At a certain conference of 100 people, there are 29 Indian women and 23 Indian men. Of these Indian people 4 arc
doctors and 24 are either men or doctors. There are no foreign doctors. How many foreigners and women doctors
are attending the conference?

Moderate

A

18,1
B

34,3
C

46,4
D

42,2

Solution

See the following Venn diagram.

$\begin{array}{ll} n (I) = 29 + 23 = 52, \\ n (F) = 100 - 52 = 48, \\ n (M \cup D) = n (M) + n (D) - n (M \cap D) \\ \Rightarrow 24 = 23 + 4 - n (M \cap D) \\ ∴ n (M \cap D) = 3 \\ ∴ n (W \cap D) = 4 - 3 = 1 \end{array}$

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