What Is a Venn Diagram? Components, Examples, and Applications

What Is a Venn Diagram?

A Venn diagram is an illustration that uses overlapping circles to show the logical relation between two or more sets of items. Circles that overlap have a commonality while circles that do not overlap do not share those traits. The Venn diagram was popularized by John Venn in the 1880s.

Venn diagrams help to visually represent the similarities and differences between two concepts. They have long been recognized for their usefulness as educational tools. Since the mid-20th century, Venn diagrams have been used as part of the introductory logic curriculum and in elementary-level educational plans around the world.

Understanding Venn Diagrams

Venn diagrams are useful for illustrating how different concepts or factors intersect with one another. They can show, at a glance, how things are similar or different and where and how they overlap. Often, the center of a Venn diagram (the intersection of two or more circles) represents some nexus or main idea that can be decomposed into the various other circles, with labels on the outer portions more distinct than those toward the center.

The overlapping areas can also be used to show where two otherwise disparate contexts share commonalities. For instance, in the example diagram below we see that while the urban and rural contexts are distinct with their own set of activities, they also share sporting events.

Venn Diagram Components

While there are many ways to organize a Venn diagram, they most often consist of overlapping circles. Each circle by itself represents a set, which may include ideas, concepts, numbers, or objects.

When circles overlap or intersect, those sub-sets that are shared are known as a union or intersection. Areas that don't overlap show differences between sets, and a complement set refers to everything not shared by a particular set or sub-set.

The History and Origin of Venn Diagrams

The English logician John Venn popularized the diagram in the 1880s. He called them Eulerian circles after the Swiss mathematician Leonard Euler, who created similar diagrams in the 1700s.

The term Venn diagram did not appear until 1918 when Clarence Lewis, an American academic philosopher and the eventual founder of conceptual pragmatism, referred to the circular depiction as the Venn diagram in his book "A Survey of Symbolic Logic."

Venn studied and taught logic and probability theory at Cambridge University, where he developed his method of using diagrams to illustrate the branch of mathematics known as set theory. He published a precedent-setting work, "The Logic of Chance," which explained the frequency theory of probability. In it, he argued that probability, contrary to popular assumption, should be established based on the regularity with which something is predicted to occur. In another book, "Symbolic Logic," Venn built on and developed mathematician George Boole’s theories on algebra. This work helped him develop the Venn diagram.

Applications for Venn Diagrams

Venn diagrams are used to depict how items relate to each other against an overall backdrop, universe, data set, or environment. A Venn diagram could be used, for example, to compare two companies within the same industry by illustrating the products both companies offer (where circles overlap) and the products that are exclusive to each company (outer circles). 

Venn diagrams are, at a basic level, simple pictorial representations of the relationship that exists between two sets of things. However, they can be much more complex. Still, the streamlined purpose of the Venn diagram to illustrate concepts and groups has led to their popularized use in many fields, including statistics, linguistics, logic, education, computer science, and business.

Examples of Venn Diagrams

A Venn diagram could be drawn to illustrate fruits that come in red or orange colors. Below, we can see that there are orange fruits (circle B) such as persimmons and tangerines while apples and cherries (circle A) come in red colors. Peppers and tomatoes come in both red and orange colors, as represented by the overlapping area of the two circles.

You might also draw a Venn diagram to help decide which of two cars to purchase. The Venn diagram shows the features that are exclusive to each car and the features that both cars have.

Below, we see that Car A is a sedan that's powered by gasoline and gets 20 miles per gallon, while Car B is a hybrid, gets 40 miles per gallon, and is a hatchback.

The shaded region where the two circles overlap shows the features that both cars have in common, which include a radio, four doors, Bluetooth capability, and airbags.

The Venn diagram graphically conveys the similarities and differences between the two cars to help decide which to purchase.

The Bottom Line

Venn diagrams are an efficient way to express the relationship between items and which attributes they have in common. Since they help visualize the similarities and differences between limited sets of things, they are widely used in education, probability, logic, statistics, linguistics, and computer science.