In a recent survey, 30 students reported whether they liked their potatoes Mashed, French-fried, or Twice-baked. 15 liked them mashed, 20 liked French fries, and 9 liked twice baked potatoes. Additionally, 12 students liked both mashed and fried potatoes, 5 liked French fries and twice baked potatoes, 6 liked mashed and baked, and 3 liked all three styles. How many students hate potatoes? (4 points)

6 students hate potatoes.

Step-by-step explanation:

The Venn diagram representing the situation is shown in the attached photo.

Set M represents the set of students that like mashed potatoes.

Set F represents the set of students that like French fried potatoes.

Set T represents the set of students that like Twice-baked potatoes.

H represents the number of students that hate potatoes.

3 liked all three styles

The number of students that like mashed and twice baked potatoes only is 6 - 3 = 3

The number of students that like mashed and French fried potatoes only is 12 - 3 = 9

The number of students that like twice baked and French fried potatoes only is 5 - 3 = 2

The number of students that like mashed potatoes only is 15 - (9 + 3 + 3) = 0

The number of students that like French fried potatoes only is 20 - (9 + 3 + 2) = 6

The number of students that like twice baked potatoes only is 9 - (3 + 3 + 2) = 1

Since the total number of students is 30, it means that

0 + 6 + 1 + 3 + 9 + 2 + 3 + H = 30

24 + H = 30

H = 30 - 24

H = 6