Q. 74.4( 70 Votes )

# 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 T be the set of people who like Tennis,

and C be the set of people who like Cricket.

Number of people who like Cricket = n(C) = 40

Number of people who like at tennis or Cricket = n(T ∪ C ) = 65

Number of people who like both tennis and Cricket = n(T ∩ C )

= 10

Number of people who like Tennis = n(T)

We know that-

n(T ∪ C) = n(T)+ n(C) - n(T ∩ C)

⇒ 65 = n(T)+40 - 10

⇒ 65 = n(T)+30

⇒ n(T) = 65-30

∴ n(T) = 35

Thus, the number of people who like tennis = 35

Now,

The number of people who like tennis only and not cricket

= Number of people who like Tennis

- Number of people who like both tennis and Cricket

= n(T) - n(T ∩ C )

= 35-10

= 25

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