Venn Diagram

Definition

A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. The points inside a curve labelled S represent elements of the set S, while points outside the boundary represent elements not in the set S. This lends to easily read visualizations; for example, the set of all elements that are members of both sets S and T, S ∩ T, is represented visually by the area of overlap of the regions S and T. In Venn diagrams the curves are overlapped in every possible way, showing all possible relations between the sets. They are thus a special case of Euler diagrams, which do not necessarily show all relations. Venn diagrams were conceived around 1880 by John Venn.

What is ‘Venn Diagram’

A Venn diagram is an illustration that utilizes circles, either overlapping or non-overlapping, to depict a relationship between finite groups of things. This diagram was named after John Venn, an English philosopher and logician, in 1880.

Explaining ‘Venn Diagram’

Venn diagrams have long been recognized for their usefulness on an educational level. Since the mid-20th century, these diagrams have been used as part of the introductory logic curriculum and in elementary-level educational plans around the world.

The History of the Venn Diagram

The English logician John Venn invented the diagram in 1880; however Venn originally called the illustration Eulerian circles. American academic philosopher, and the eventual founder of conceptual pragmatism, Clarence Lewis referred to the circular depiction as the Venn diagram in his book “A Survey of Symbolic Logic” in 1918.

While Venn diagrams are, at a basic level, simple pictorial representations of the relationship that exists between two sets of ‘things’, they are much more complex in both their orientation and their applications. Still, the streamlined purpose of the Venn diagram has led to their popularized use to illustrate concepts and groups and are considered trademark tools for the teaching of beginner-level logic and math.

An Example

Consider drawing a Venn diagram to consider four-legged animals and domesticated animals. Obviously, there are a vast number of animals with four legs. But how many of such animals have been domesticated? Dogs and cats would be two examples of four-legged creatures that would fall in the overlapping space of the two circles. A tiger, however, would reside only in the circle representing four-legged animals. A chicken would be an example of a domesticated animal that does not have four legs and thus would exist only in the circle representing domesticated animals.