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Home » 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?
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?
CBSE | Class 11 | Exercise 1.6 | Maths | NCERT | Sets
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?

Solution:

Let’s consider C as the set of people who like cricket, and
the set of people who like tennis as T.

n(C~\cup ~T)\text{ }=\text{ }65

n\left( C \right)\text{ }=\text{ }40

n(C~\cap ~T)\text{ }=\text{ }10

This can be written as

n(C~\cup ~T)\text{ }=~n\left( C \right)\text{ }+~n\left( T \right)-~n(C~\cap ~T)

Now, substitute the values

65\text{ }=\text{ }40\text{ }+~n\left( T \right)-10

Calculating further

65\text{ }=\text{ }30\text{ }+~n\left( T \right)

As a result, we get

n\left( T \right)\text{ }=\text{ }65-30\text{ }=\text{ }35

As a result, 35 people like tennis.

It is known that,

\left( T-C \right)~\cup ~(T~\cap ~C)\text{ }=\text{ }T

As a result, we get,

\left( T-C \right)~\cap ~(T~\cap ~C)\text{ }=~\Phi

Now, here

n~\left( T \right)\text{ }=~n~\left( T-C \right)\text{ }+~n~(T~\cap ~C)

Substitute the values

35\text{ }=~n~\left( T-C \right)\text{ }+\text{ }10

Calculating further

n~\left( T-C \right)\text{ }=\text{ }35-10\text{ }=\text{ }25

As a result, 25 people like only tennis.

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