class=skin-invert-image|thumb|Venn diagram showing the uppercase [[glyphs shared by the Greek (upper left), Latin (upper right), and Russian Cyrillic (bottom) alphabets]]

A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram uses simple closed curves on a plane to represent sets. The curves are often circles or ellipses.

Very similar ideas had been proposed before Venn such as by Christian Weise in 1712 (Nucleus Logicoe Wiesianoe) and Leonhard Euler in 1768 (Letters to a German Princess). The idea was popularised by Venn in Symbolic Logic, Chapter V "Diagrammatic Representation", published in 1881.

Details

A Venn diagram, also called a set diagram or logic diagram, 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 itself to intuitive visualizations; for example, the set of all elements that are members of both sets S and T, denoted S ∩ T and read "the intersection of S and T", is represented visually by the area of overlap of the regions S and T. Euler diagrams, which are similar to Venn diagrams but do not necessarily contain all possible unions and intersections, were named after the mathematician Leonhard Euler in the 18th century. can also be clearly traced back to the 16th century. Pioneers in this tradition of Euler diagrams included Erhard Weigel (1625–1699) and his students Johann Christoph Sturm (1635-1703) and Gottfried Wilhelm Leibniz (1646–1716). Christian Weise (1642–1708) is also worth mentioning, whose student Johann Christian Lange worked intensively on these diagrams.

Venn did not use the term "Venn diagram" and referred to the concept as "Eulerian Circles". In the opening sentence of his 1880 article Venn wrote that Euler diagrams were the only diagrammatic representation of logic to gain "any general acceptance". Similar methods were then adopted in mathematics and subsequently in computer science.

Venn diagrams have been commonly used as a format for internet humor. One of the earliest recurring examples appeared in 2006 on Indexed, a blog by writer and illustrator Jessica Hagy in which she used hand-drawn Venn diagrams on index cards to offer jokes and social commentary. Time magazine named Indexed one of its 25 best blogs in 2007, describing it as using Venn diagrams to "graphically and (often hilariously) highlight life's profundities and absurdities." In August 2018, a Venn diagram comparing phrases used by preachers, DJs, and bank robbers spread across Twitter, Facebook, and Reddit, inspiring numerous user-created variations and being documented as a recurring meme format. At least one politician has been mocked for misusing Venn diagrams.

Overview

<div class=skin-invert-image></div>

A Venn diagram is constructed with a collection of simple closed curves drawn in a plane. According to Lewis,

References

Further reading

  • (NB. The book comes with a 3-page foldout of a seven-bit cylindrical Venn diagram.)
  • Lewis Carroll's Logic Game – Venn vs. Euler at Cut-the-knot
  • Six sets Venn diagrams made from triangles
  • Interactive seven sets Venn diagram
  • VBVenn, a free open source program for calculating and graphing quantitative two-circle Venn diagrams
  • InteractiVenn, a web-based tool for visualizing Venn diagrams
  • DeepVenn, a tool for creating area-proportional Venn Diagrams