Question

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 1

Let T is the set of people who like Tennis,
and C is 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)

use formula,
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

Answer 2

Answer:

25

Step-by-step explanation:

Let the number of people who like cricket n(C) = 40

number of people who like tennis n(T) = ?

number of people in the group n(C∪T) = 65

number of people who like both

Cricket and Tennis = n(C∩T) = 10

number of people who like only

tennis and not cricket = n( C∪T ) - n(C) = ?

We know that ,

n(C) + n(T) = n(C∩T) + n(C∪T)

⇒40 + n(T) =  10 + 65

⇒ n(T) = 75 - 40

= 35

Number of people who like tennis

only not cricket = n( C∪T ) - n( C )

= 65 - 40

= 25

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