# What Is a Venn Diagram? Meaning, Examples, and Uses

![Venn Diagram](https://www.investopedia.com/thmb/7BwAf5Ti-5HWC3yMPT2hiNE6ap0=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/VennDiagram-a055088ccae84801bfefe8ec90ff866b.jpg)

*— Investopedia / Xiaojie Liu*

> **Definition**
>
> A Venn diagram uses overlapping circles to graphically illustrate the traits that are shared and not shared by two or more sets of things being compared.

## What Is a Venn Diagram?

A Venn diagram is a graphic that identifies the traits that two or more sets of things, concepts, or people share and don't share. Circles representing each trait overlap when they share traits. Circles that do not overlap have no common traits.

The Venn diagram was popularized by mathematician John Venn in the 1880s and is still widely used.

### Key Takeaways

*   Venn diagrams show at a glance the similarities and differences between concepts, things, or people.
*   The commonalities appear in the area of overlap, known as the intersection.
*   Venn diagrams are widely used in business and in many academic fields.

## How Venn Diagrams Work

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.

For instance, in the diagram below we can see that while urban and rural areas have many different attributes, sports activities can be found in both.

![Venn Diagram](https://www.investopedia.com/thmb/w0LO4PhZUkMNbFMmVQGO1DTZbUI=/630x0/filters:no_upscale():max_bytes(150000):strip_icc()/countrycity-56a4b8b03df78cf77283f15c.JPG)

*Venn Diagram (click to enlarge).*

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

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

## The History and Origin of Venn Diagrams

John Venn, an English mathematician and logician, popularized the diagram that bears his name. His work was influenced by Swiss mathematician Leonhard Euler, whose diagrams are known as Euler diagrams. Euler's diagrams also represent logical relationships but do not necessarily use all possible intersections of sets, which is a defining feature of Venn diagrams.

Venn studied and taught logic and [probability](https://www.investopedia.com/terms/p/probabilitydistribution.asp) theory at Cambridge University, where he developed his method of using diagrams to illustrate the branch of mathematics known as set theory.

In 1866, Venn published a groundbreaking work, "The Logic of Chanc_e_," which explained his frequency theory of probability, arguing that probability should be based on the frequency with which something can be predicted to occur over time. In another book, "Symbolic Logic," Venn built on and developed mathematician George Boole's theories on [algebra](https://www.investopedia.com/terms/a/algebraic-method.asp). This work helped him advance the concept of the Venn diagram.

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."

## Applications for Venn Diagrams

Venn diagrams depict how items relate to one another against an overall backdrop, universe, data set, or environment.

A Venn diagram could be used, for example, to compare two companies in 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 simple pictorial representations of the relationship that exists between two sets of things. Their ease of use led to their widespread popularity for sharing information in fields including [statistics](https://www.investopedia.com/terms/s/statistics.asp), linguistics, logic, education, computer science, and business.

## Examples of Venn Diagrams

As an example, a Venn diagram could distinguish between fruits and vegetables that come in red and/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.

![Image 1](https://www.investopedia.com/thmb/fkBAVOk2DzJcX31hcM-iKJxzZCg=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/VennDiagram1_2-6b1d04d5b6874b4799b1e2f056a15469.png)

**

You might also draw a Venn diagram to help decide which of two cars to purchase. The Venn diagram below shows the features that are exclusive to each car and the features that both cars have. 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 that gets 40 miles per gallon and is a hatchback.

![Image 2](https://www.investopedia.com/thmb/KIYyHGh894f8cXJkIR4tlVbFHAk=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/VennDiagram2-dcf415cf11cf4cd1b03b522a984d9516.png)

**

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

Depending on which features are important to you, the Venn diagram shows clearly what each car has (and doesn't have).

## What Is a Venn Diagram in Math?

A Venn diagram in math can show how various sets of numerical data overlap with one another.

For example, if one circle represents every number between 1 and 25 and another represents every number between 1 and 100 that is divisible by 5, the overlapping area would contain the numbers 5, 10, 15, 20, and 25, while all the other numbers would be confined to their separate circles.

## How Do You Read a Venn Diagram?

A Venn diagram is read by observing all of the circles that make up the entire diagram. Each circle is its own item or data set. The portions of the circles that overlap indicate the areas that are in common among the different items while the parts that do not overlap indicate the unique traits of each item.

## Does a Venn Diagram Always Use Two or Three Circles?

Venn diagrams can use any number of circles (or any other shape) to show the differences and intersections of multiple sets, although the diagram may become unwieldy and hard to read when more than a few sets are included.

## The Bottom Line

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

> **Article Sources**
>
> 1.  LibreText Mathematics. "[3.1.2: Venn Diagrams](https://math.libretexts.org/Courses/Rio_Hondo/Math_150%3A_Survey_of_Mathematics/03%3A_Logic/3.01%3A_Basics_of_Sets/3.1.02%3A_Venn_Diagrams)."
>     
> 2.  Research in History and Philosophy of Mathematics. "[Origins of the Venn Diagram](https://logic-teaching.github.io/pred/texts/Bennett%202015%20-%20Origins%20of%20the%20Venn%20Diagram.pdf)," Page 112.
>     
> 3.  Encyclopedia Britannica. "[John Venn](https://www.britannica.com/biography/John-Venn#ref1085272)."
>     
> 4.  Project Gutenberg. "[The Logic of Chance, 3rd Edition](https://www.gutenberg.org/cache/epub/57359/pg57359-images.html)."
>     
> 5.  Google Books. "[Symbolic Logic](https://www.google.com/books/edition/_/VrARAAAAYAAJ?hl=en&gbpv=1&pg=PR1)."
>     
> 6.  Internet Archive. "[A Survey of Symbolic Logic](https://archive.org/details/asurveyofsymboli00lewiuoft/page/n7/mode/2up)."