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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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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?

Answer

Let \(C\) denote the set of people who like cricket, and \(T\) denote the set of people who like tennis
\(∴ \)\(n(C ∪ T) = 65, n(C) = 40, n(C ∩ T) = 10\)
\(n(C ∪ T) = n(C) + n(T) – n(C ∩ T)\)
\(∴ 65 = 40 + n(T) – 10\)
\(⇒ 65 = 30 + n(T)\)
\(⇒ n(T) = 65 – 30 = 35\)
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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