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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 ______.
Options
0
25
35
45
Solution
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 25.
Explanation:
Total number of students = 60
⇒ n(U) = 60
Number of students who play Cricket = 25
⇒ n(C) = 25
Number of students who play Tennis = 20
⇒ n(T) = 20
Number of students who play Cricket and Tennis both = 10
⇒ n(C ∩ T) = 10
∴ n(C ∪ T) = n(C) + n(T) – n(C ∩ T)
= 25 + 20 – 10
= 45 – 10
= 35
∴ n(C' ∩ T') = n(U) – n(C ∪ T)
= 60 – 35
= 25
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