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 C be the set of people who like cricket and T who like tennis
Here, `n (C) = 40`
`:. n(C cup T) = 65 and n (C cap T) = 10`
Number of people who like only tennis but not cricket
`= n(C cupT)-n(C)`
`=65-40=25`
Again `n(C cupT)=n(C)+n(T)-n(C cap T)`
`rArr 65=40 +n(T) -10`
`rArr n(T)=65-40 +10 = 35`
and number of people who like tennis = 35.