First slide

Introduction to Sets

Question

In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is

Easy

A

22
B

33
C

10
D

45

Solution

$\begin{array}{l} n (M) = 55, n (P) = 67, n (M \cup P) = 100 \\ Now, n (M \cup P) = n (M) + n (P) - n (M \cap P) \\ 100 = 55 + 67 - n (M \cap P) \\ ∴ n (M \cap P) = 122 - 100 = 22 \\ n (P only) = n (P) - n (M \cap P) = 67 - 22 = 45 \end{array}$

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