In a group of 65 people, 40 like cricket, 10 like both cricket and tennis.
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?

Solution:

Let C denote the set of people who like cricket, and

T denote the set of people who like tennis

∴ n(C  T) = 65, n(C) = 40, n(C  T) = 10

We know that:

n(C  T) = n(C) + n(T) – n(C  T)

∴ 65 = 40 + n(T) – 10

⇒ 65 = 30 + n(T)

⇒ n(T) = 65 – 30 = 35

Therefore, 35 people like tennis.

Now,

(T – C)  (T  C) = T

Also,

(T – C)  (T  C) = Φ

∴ n (T) = n (T – C) + n (T  C)

⇒ 35 = n (T – C) + 10

⇒ n (T – C) = 35 – 10 = 25

Thus, 25 people like only tennis.

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