Wednesday, November 23, 2011

Venn diagram

A Venn diagram or set diagram is a diagram that shows all hypothetically possible logical relations between a finite collection of sets (aggregation of things). Venn diagrams were conceived around 1880 by John Venn. They are used to teach elementary set theory, as well as illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.

Venn diagrams normally comprise overlapping circles. The interior of the circle symbolically represents the elements of the set, while the exterior represents elements which are not members of the set. Shapes other than circles can be employed, and this is necessary for more than three sets. Venn diagrams do not generally contain information on the relative or absolute sizes (cardinality) of sets; i.e. they are schematic diagrams.

Venn diagrams were introduced in 1880 by John Venn (1834–1923) in a paper entitled "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings" in the "Philosophical Magazine and Journal of Science", about the different ways to represent propositions by diagrams. The use of these types of diagrams in formal logic, according to Ruskey and M. Weston (2005), is "not an easy history to trace, but it is certain that the diagrams that are popularly associated with Venn, in fact, originated much earlier. They are rightly associated with Venn, however, because he comprehensively surveyed and formalized their usage, and was the first to generalize them".

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