Venn Diagrams 101


Definition, Examples, and Uses

What is a Venn Diagram?

Sources like Wikipedia provide a somewhat complex mathematical definition of the Venn Diagram that comes from the world of Set theory. However, when most of us encounter Venn Diagrams they are being used to depict a specific simple concept: The overlap between two populations.

Venn Diagrams consist of multiple overlapping closed curves. In the most common cases, like the one above, this is takes the form of two overlapping circles. Each circle represents a population of some sort, and the diagram then is able to visually represent three distinct groups: things only in population A, things only in population B, and things that belong to both populations.

Venn Diagrams are a powerful visual aid, and they are somewhat unique in that they can be used to effectively represent the mathematical magnitude of an overlap, as well as conceptual overlaps of ideas or other qualitative things. The examples below help show some of these unique uses of the Venn Diagram.

Venn Diagram Examples

Meta Venn Diagram

This one is a bit tongue-in-cheek, but demonstrates how the Venn Diagram can be used to show a more qualitative association between of overlapping concepts. It's true, not all circles are diagrams and not all diagrams involve circles, but Venn Diagrams exist at the intersection of these things.

Sets: States and Elements

This is actually a great example of how Venn Diagrams are used in Set theory. Unlike some of the abstract concepts shown in other examples, this diagram is actually depicting two finite sets: the abbreviations of the US states and the symbols of the chemical elements in the periodic table. As it turns out, 16 of these seemingly unrelated items share the same abbreviation.

Characteristics

Venn Diagrams can also be used to indicate the shared and disparate characteristics of two things. In this case, birds and bats are profiled by both their similarities and differences in a single visual.

Market Position

Over the years, many brands have used Venn Diagrams as a way to communicate their unique value proposition to their market. The diagram below was an early logo for Rap Genius that depicted its offering as being “Wikipedia meets Rap Lyrics meets Urban Dictionary.”

Cylinder Venn Diagrams

Venn Diagrams aren’t just used to show slight overlaps. They can also be useful for showing how subsets within a larger set are differentiated. The “Cylinder Venn Diagram” below gives a clear representation of different regions of the British Islands, and does so far more succinctly than could be accomplished with words.

No Overlap

Venn diagrams also come in the form of non-overlapping circles, although these diagrams largely defeat the purpose of the diagram in the first place. They are most likely presented for the purpose of making a point or a joke rather than demonstrating a mathematical relationship.

Many Circles

As our final example, Venn Diagrams can also be depicted with many circles, creating intersections of each pair of circles along with a center point where all the circles interact. By moving the position of each circle, different permutations can emerge to fit the situation.

Conclusion

Venn Diagrams are a powerful example of how a mathematical construct can actually be used to depict things well beyond the world of numbers and sets. They give us the perspective to see similarities in disparate ideas, while allowing us to identify the differentiators in seemingly unremarkable things. From pop culture to religion to science to comedy, they have changed the way we think and communicate.