First slide

Operations on Sets

Question

In a class of 30 pupils, 12 take needle work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three then the number of pupils taking 2 subjects is

Easy

A

16
B

6
C

8
D

20

Solution

Given $n (N) = 12, n (P) = 16, n (H) = 18, n (N \cup P \cup H) = 30$
From, $n (N \cup P \cup H) = n (N) + n (P) + n (H) - n (N \cap P)$
$- n (P \cap H) - n (N \cap H) + n (N \cap P \cap H)$
$∴ n (N \cap P) + n (P \cap H) + n (N \cap H) = 16$
Now, number of pupils taking two subjects
$= n (N \cap P) + n (P \cap H) + n (N \cap H) - 3 n (N \cap P \cap H)$
$= 16 - 0 = 16 .$

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