In a class of 60 students, 25 students play cricket and 20 students play tennis and 10 students play both the games.

Question:

In a class of 60 students, 25 students play cricket and 20 students play tennis and 10 students play both the games. Then the number of students who play neither is

(a) 0

(b) 25

(c) 35

(d) 45

Solution:

Let ⋃ denote the universal set

Let C denote the set of students playing circket

Let T denote the set of students playing tennis

n(⋃) = 60, n(C) = 25, n(T) = 20

n(C⋂T) = 10

Then n(C⋃T)n(⋃) – n(C⋃T)

n(⋃) – [n(C) + n(T) – n(C⋂T)]

= 60 – [25 + 20 – 10]

= 60 – [45 – 10]

= 60 – 35

n(C⋃T)= 25

Hence, the number of students who play neither crickets nor tennis is 25

Hence, the correct answer is option B.

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