Question

In a group of 65 people, 40 were found to like hockey, 10 like both tennis and hockey. How many like only tennis but not hockey ? How many like tennis? Represent using venn diagram
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Answer 1

Step-by-step explanation:

Now, let us find a number of people who like tennis. For this, let C and T denote a set of people who like cricket and tennis respectively.

We are given a number of people = 65.

Therefore, the number of people who like cricket or tennis = 65.

Thus, n(C∪T)=65⋯⋯⋯⋯⋯(1)

Also, we are given that, the number of people who like cricket is 40.

Thus, n(C)=40⋯⋯⋯⋯⋯(2)

Also, the number of people who like both tennis and cricket is 10.

Thus, n(C∩T)=10⋯⋯⋯⋯⋯(3)

As we know, for any two set

n(A∪B)=n(A)+n(B)−n(A∩B)

So, let's use it for set C and T, we get:

n(C∪T)=n(C)+n(T)−n(C∩T)

Putting value from (1), (2) and (3) we get:

65=40+n(T)−10⇒65=30+n(T)⇒n(T)=35

n(T) represents the number of people who like tennis.

Therefore, the number of people who like tennis = 35.

The number of people who like only tennis but not cricket = number of people who like tennis - the number of people who like both cricket and tennis.

⇒n(T)−n(T∩C)⇒35−10⇒25

Hence, 25 people like only tennis and not cricket.

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Answer 2

Step-by-step explanation:

15 people's like tennis