Question 7:
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
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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