Many things can be arranged into overlapping sets.

John Venn invented the Venn diagram in 1881. These drawings are used to illustrate characteristics of data sets. Although primarily used in set theory, they have found wider application in probability, linguistics, logic, statistics and computer science by virtue of being simple and intuitive.

Venn diagrams are most useful when comparing two or more sets with overlapping features. For example, if you want to compare students who speak French and English, you can divide them into sets: students who speak French, students who speak English and students who speak both languages.

## Instructions

1. Draw a box. On a right-hand corner, write “E.” The E represents a universal set. In this example, it includes all students: French speakers and English speakers.

2. Draw a circle inside the box. For the purpose of this example, label it “English.” If you are comparing different sets, label it accordingly.

3. Draw another circle and label it. This is the second set. In this example, call it “French.” Make sure that the two circles overlap. In set theory, the overlap is known as the intersection of sets and is often shaded to make it visually apparent.

4. Calculate the numbers that belong to the first set minus the overlap — that is, the number of English speakers who do not speak French. You can find this number by subtracting the number of students who speak both languages from the total number of English speakers. Write this number in the middle of the English circle, but outside of the overlap.

5. Determine the number in the second set, minus the numbers that overlap. In the example, it is the number of students who speak only French. Write this number in the middle of the French circle, but outside of the overlap.

6. Calculate the number belonging to both sets. In the example, this is the number of students who speak both languages. Write this number in the middle of the overlapping area. The simple Venn diagram is now complete.

7. Go to MIT’s Venn Diagram Generator Web page and enter the values of different sets. The Web page will create a simple Venn diagram.