Question

in a group of friends,1/2 liked to play football and 3/4 liked tennis.If 35 friends in the group likesd both tennis and football,how many liked tennis only?​

Answer 1

Step-by-step explanation:

Let C denote the set the people like cricket, and T denote the set of people who like tennis

∴n(C∪T)=65,n(C)=40,n(C∩T)=10

We know that

n(C∪T)=n(C)+n(T)−n(C∩T)

∴65=40+n(T)−10

⇒65=30+n(T)

⇒n(T)=65−30=35

Therefore, 35 people like tennis.

Now,

n(T−C)=n(T)−n(T∩C)

⇒n(T−C)=35−10=25

Thus, 25 people like only tennis.