Question

in a group of 65 people , 40 likes cricket,10 likes both cricket and tennis . how many like tennis only and not cricket ? how many likes tennis ?

Answer 1

Let C be the set of people who like cricket.

Let T be the set of people who like tennis.

Given:

n(C U T) = 65 People

n(C) = 40 People

n(C ⋂ T) = 10 People

To Find:

n(T) = ?

Calculating:

The formula that is used to calculate the union of sets:

n(C U T) = n(C) + n(T) - n(C ⋂ T)

Taking n(C) and - n(C ⋂ T) to the other side of the formula we get:

n(T) = n(C U T) - n(C) + n(C ⋂ T)

Substituting all the values known to us in this formula we get:

n(T) = 65 - 40 + 10

n(T) = 25 + 10

n(T) = 35

Therefore, 35 People like Tennis.

Now,

Calculating the number of people that like tennis only and not cricket:

By using the formula:

= n(T) - n(T ⋂ C)

Substituting the values known to us in this formula we get:

= 35 - 10

= 25

Therefore, 25 people like Tennis only and not Cricket.