What Is a Venn Diagram?

A Venn diagram is a graphic that uses overlapping circles to identify traits that are shared bet♊ween two or more sets of things and traits that are not shared. Circles that do not overlap have no common traits.

The Venn diagram was popularized by John Venn in the 188꧟0s and is still widely used to illustrate the distinctions and commonalities among con𝓡cepts, people, or things.

How Venn Diagrams Work

Venn diagrams are useful for illustrating how d🅠ifferent 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 see that while urban and rural areas are distinct and have their own sets of activities, they also share sporting events in common.

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 consist 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 logician, popularized the diagram that bears his name. The diagrams were named after him, and while they were influenced by the work of the Swiss mathematician Leonhard Euler, Euler's diagrams are distinct and are known as "Euler diagrams." Euler's diagrams also represented logical relationships but did not necessarily use all possible intersections of sets, which is a defining feature of Venn diagrams.

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. In 1866, he published a groundbreaking work, "The Logic of Chance," 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. 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 are used to 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 within the same industry by illustrating the products both companies offer (where circles overlap) and the products that are exc🦄lusive 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 澳洲幸运5开奖号码历史查询:statistics, 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, whiꦜle aღpples 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 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, 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 four doors, a radio, Bluetooth c𓃲apability, and airbags.

Depending on which features are important to you, the Venn diagram can graphically convey what the two cars have (or don't have) to offer.

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 business, education, probability, logic, statistics, linguistics, and computer science.