In a group of 65 people, 40 like cricket, 10 ...

NCERT Class XI Mathematics - Sets - Solutions

Question : 56 of 73

Marks: +1, -0

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 be the set of people who like cricket and T be the set of people who like tennis.

Here n(C) = 40, n(C ∩ T) = 10 and n(C ∪ T) = 65

We know that n(C ∪ T) = n(C) + n(T) – n(C ∩ T)

⇒ 65 = 40 + n(T) – 10 ⇒ n(T) = 65 – 30 = 35

∴ Number of people who like tennis = 35

Now number of people who like tennis only and not cricket

= n(T – C) = n(T) – n(C ∩ T) = 35 – 10 = 25.

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