# Venn Diagram example

On this page, we provide a demonstration of how to solve a Venn diagram question using the Venn diagram maker.

In a school, there are 220 students in total. Out of these, 132 students learn math, 95 students learn physics, and 60 students learn drama. 30 students study both math and physics, 22 students study both math and drama, and 35 students study both physics and drama. There are also 10 students who have taken subjects other than math, physics, or drama.

1. How many students study only math and physics?
2. How many students study only math and drama?
3. How many students study only physics and drama?
4. How many students study all three subjects?

#### Solutions:

1. The default is 3 groups
2. Select 'Number of data items' in 'input' field.
3. Enter School in 'Title' field.
4. Total - Enter 220 in 'All' field.
5. Group-A
• Enter 'Math' label, the default is 'A'
• Enter 132 in 'All' field
6. Group-B
• Enter 'Physics' label, the default is 'B'
• Enter 95 in 'All' field
7. Group-C
• Enter 'Drama' in 'name' field, the default is 'C'
• Enter 60 in 'All' field
8. The intersections labels will be calculated automatically, but you may override it.
9. Group-A ∩ Group-B - Enter 30 in 'All' field.
10. Group-A ∩ Group-C - Enter 22 in 'All' field.
11. Group-B ∩ Group-C - Enter 35 in 'All' field.
12. Group-A ∩ Group-B ∩ Group-C - Enter 'All' label, the default is 'Math ∩ Physics ∩ Drama'. You may leave it as the default.

Until now the calculator couldn't calculate any number. you should have the following screen:

13. No group - Enter 10 in 'All' field.
Now the calculator had enough data to calculate other numbers, it entered the calculated numbers in brown.

### Solution

The calculator shows the solution bellow the form. We suggest you also look at the Venn diagram below for a better understanding.

1. At least one = Total - No group = 220 - 10 = 210
2. A∩B∩C = Total - No group - A - B - C + A∩B + A∩C + B∩C = 220 - 10 - 132 - 95 - 60 + 30 + 22 + 35 = 10
3. A∩C only = A∩C - A∩B∩C = 22 - 10 = 12
4. A∩B only = A∩B - A∩B∩C = 30 - 10 = 20
5. A only = A - A∩C only - A∩B only - A∩B∩C = 132 - 12 - 20 - 10 = 90
6. B∩C only = B∩C - A∩B∩C = 35 - 10 = 25
7. C only = C - A∩C only - B∩C only - A∩B∩C = 60 - 12 - 25 - 10 = 13
8. B only = B - A∩B only - B∩C only - A∩B∩C = 95 - 20 - 25 - 10 = 40
1. 20 students study only math and physics. (A∩B only)
2. 12 students study only math and drama. (A∩C only)
3. 25 students study only physics and drama. (B∩C only)
4. 10 students study all three subjects. (A∩B∩C only)

#### Venn Diagram

Press 'Calculate' button to get the venn diagram solution: