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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