Venn diagrams use overlapping shapes (usually circles) that illustrate a logical relationship between two or more sets of items. Often, a Venn diagram serves to organize things in a graphical form, and highlight similarities or differences between certain items.

## What Is a Venn Diagram?

Venn diagrams, otherwise called Logic or Set diagrams, can be used in statistics, mathematics, business, computer science, teaching, logic, and linguistics. Venn diagrams gained wide popularity in the 1960s when they became a part of the so-called “new math” curricula. A Venn diagram usually looks like a simple scheme, which involves two-three sets of several elements. Sometimes, such diagrams gain six or more sets and evolve into the form of 3D presentations, looking rather sophisticated. Venn diagrams encourage us to think things through while depicting the relations of items within a particular segment or a “universe”. A Venn diagram allows a user to visualize their data in a powerful and clear way, which makes them a popular choice for reports and presentations. This type of diagrams has much in common with Euler diagrams that only differ by leaving out sets without any items. Venn diagrams, on the contrary, tend to show all relations, even the empty sets.

## History of Venn Diagrams

Venn diagrams got their name after John Venn, a British logician. The first time Venn mentioned them was in his 1880 paper on diagrams and problems of representation of reasoning and propositions.

However, scientists believe that Venn diagrams have a longer history. According to a 1969 research article by M. E. Baron, the 13^{th}-century Majorcan logician and philosopher, Ramon Lull was the first to use a similar diagram. Besides, Baron also credits a German mathematician G. Wilhelm for drawing similarly looking diagrams at the end of 17^{th} century.

In the 18^{th} century, a mathematician from Sweden, Leonard Euler, invented the type of diagrams, which later were called after him, and became the direct forerunner of Venn diagrams. What’s interesting, John Venn used to call his diagrams Eulerian circles. As a term, Venn diagram was first mentioned in a 1918 book by an American logician C.I. Lewis.

Venn Diagrams kept evolving throughout the 20^{th} century with such prominent experts as D.W. Henderson, C.D. Savage, H.J.S. Smith, and many others developing and advancing them.

## An Example of a Venn Diagram

Let’s say your family is discussing summer vacation plans, and you want to choose a destination which all family members would like to visit.

- Set A includes your own (Family Member A) choices: England, Italy, France.
- Set B includes choices of Family Member B: Australia, Canada, Italy.
- Set C includes choices of Family Member C: Japan, Italy, Greece, Australia.

The intersection, or overlap, of the three sets includes only Italy. Looks like next summer your family is visiting sunny Italy.

That’s just a simple example, but sure thing, Venn diagrams can be more involved and extensive than this and are used in most various fields.

## Purpose and Benefits of Venn Diagrams

**Organizing information visually.**The visual organization helps to mark relations between two or more sets of items. Both professionals and students use Venn diagrams to think over a concept’s logic and choose relations of visual communication.**Comparing two choices**to clearly see their similarities as opposed to their distinguishing features. This is done when one needs to select an important service or product to purchase.**Solving complex problems in mathematics.****Comparing sets of data,**to spot correlations between them and predict the chances of some occurrences to happen.**To reason through the logic**for certain equations and statements.

## Venn Diagram Cases of Use

**Mathematics:**Diagrams are widely used both in schools (to explain basic concepts of math) and in advanced mathematics (for solving complex problems).**Probability and statistics:**Venn diagrams are used by experts to predict the likelihood of certain occurrences, which refers to the branch of predictive analytics.**Logic:**Diagrams help to determine how valid certain conclusions and arguments are. They are also used in deductive reasoning.**Linguistics:**Diagrams help in studying the differences and commonalities amongst various languages.**Reading comprehension:**Teachers may use Venn diagrams to help students improve their reading comprehension skills.**Computer science:**Diagrams are used in programming for visualization of hierarchies and computer languages.**Business:**Diagrams help to contrast and compare various services, products, and They also serve as an effective tool of communication and illustration.

## Glossary for Venn Diagrams

**Set**– basically, a collection of many things; things can be called objects, items, members, etc.**Union**– a set which includes all items.**Intersection**– items overlapping each other in a set.**Symmetric difference of two sets**– everything save the intersection (a subset).**Relative complement**– something in one, but not in the other set.**Absolute complement**– everything outside of the set.**Reuleaux triangle**– a common shape, formed by the intersection of three shapes.**Scaled Venn diagram**– otherwise known as Area Proportional. A number of shapes, sized by proportion to represent one whole.**Set notations**– math notions that help to represent the illustrated concept.**Set theory**– a branch in mathematics that deals with diagram sets.

## A Few Fun Facts: Venn Diagrams Hit the Small Screen

Venn diagram is one of a few that have found their place in the modern pop culture.

**In drama:** a character of CBS TV series “Numbers” (2005-2010) uses a Venn diagram to find out which suspect matches a description.

**In comedy:** The comedian Seth Meyers on his Late Night show on NBC sometimes uses Venn diagrams to find funny commonalities between unrelated items.

## Learn to Draw Basic Venn Diagrams

- Determine what and why you’d like to compare. This way you’ll define the sets.
- Make a list of the items in your sets; handwrite them or use online programs.
- Contrast and compare your sets with the diagram. Make decisions, observations, and choices now that you can see everything in a new, clear way.