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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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Best answer

Let C – Cricket; T – Tennis be the sets.

Given;

n(C’ ∪ T) = 65; n(C) = 40; n(C ∩ T) = 10

n(C ∪ T) = n(C) + n(T) – n(C ∩ T)

⇒ 65 = 40 + n(T) – 10 

⇒ n(T) = 35

n (tennis only and not cricket)

= n(T ∪ C’) = n(T) – n(T ∩ C) = 35 – 10 = 25.

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