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

Answer 1

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.