Question

In a survey of 257 college students, it is found that 69 like brussels sprouts, 91 like broccoli, 55 like cauliflower, 25 like both brussels sprouts and broccoli, 20 like both brussels sprouts and cauliflower, 21 like both broccoli and cauliflower and 15 of the students like all three vegetables. How many of the 257 college students do not like any of these three vegetables?

Answer 1

93

Explanation:

Let

U=Universal set=257

A= Brussels sprouts

B= Broccoli

C= Cauliflower

`n(A)=69`

`n(B)=91`

`n(C)=55`

`n(A\cap B)=25`

`n(B\cap C)=20`

`n(A\cap C)=21`

`n(A\cap B\cap C)=15`

We have to find the number of students who do not like any of these three vegetables.

We know that

`n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)`

Substitute the values then we get

`n(A\cup B\cup C)=69+91+55-25-20-21+15=164`

`n(A\cup B\cup C)'=U-n(A\cup B\cup C)=257-164=93`