# Venn Diagram

## DEFINITION of '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.

The basic structure of the Venn diagram is typically overlapping circles, with items in the overlapping section bearing a commonality. Items residing in the outer portions of the circles do not share specified common traits.

## BREAKING DOWN '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.

Venn studied and taught logic and probability theory at Cambridge University. This is where Venn developed his method of utilizing diagrams to illustrate set theory. Venn published a prolific, precedent-setting work "The Logic of Chance," a book that put forth the frequency theory of probability. Venn touted that probability should be established based on the regularity that something is predicted to occur, contrary to popular educated assumptions. Venn also developed and more fully realized mathematician George Boole’s theories in his book "Symbolic Logic" in 1881. This book was also the work in which Venn highlighted what would eventually become the Venn diagram.

## More About Venn Diagrams

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.