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

Answer:

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.

Answer 2

Answer:

Answer: 25 people like tennis only and not cricket.

35 people like tennis.

Step-by-step explanation:

n(C) = 40

n(C intersection T) = 10

n(CUT) = 65

USING SET FORMULA,

n(T) = n(CUT) - n(C) + n(C intersection T) = 65-40+10

= 35.

therefore 35 people like tennis. n(T-C) = 35-10

= 25.

hence, 25 people like only tennis and not

cricket

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Step-by-step explanation:

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