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Question

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

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Solution

Let C denote the set of people who like cricket, T denote the set of people who like tennis.
n(CT)=65,
n(C)=40
n(CT)=10
We know that,
n(CT)=n(C)+n(T)n(CT)
65=40+n(T)10
65=30+n(T)
n(T)=6530=35
Therefore, 35 people like tennis.
Now,
(TC)(TC)=T
Also,
(TC)(TC)=ϕ
n(T)=n(TC)+n(TC)
35=n(TC)+10
n(TC)=3510=25
Thus, 25 people like only tennis.

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