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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.
The Venn diagram is constructed with a collection of simple closed curves drawn in the plane. The principle of these diagrams is that classes be represented by regions in such relation to one another that all the possible logical relations of these classes can be indicated in the same diagram.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
Inclusion–exclusion illustrated by a Venn diagram for three sets. Generalizing the results of these examples gives the principle of inclusion–exclusion. To find the cardinality of the union of n sets: Include the cardinalities of the sets. Exclude the cardinalities of the pairwise intersections.
John Venn, FRS, [2] [3] FSA [4] (4 August 1834 – 4 April 1923) was an English mathematician, logician and philosopher noted for introducing Venn diagrams, which are used in logic, set theory, probability, statistics, and computer science.
In set theory the Venn diagrams tell, that there is an element in one of the red intersections. (The existential quantifications for the red intersections are combined by or. They can be combined by the exclusive or as well.) Relations like subset and implication, arranged in the same kind of matrix as above. In set theory the Venn diagrams tell,
The following 21 pages use this file: Algebra; Contraposition; Event (probability theory) Inclusion map; Set (mathematics) Subset; Talk:Assyrian people/Archive 7
Many of these types of diagrams are commonly generated using diagramming software such as Visio and Gliffy. Diagrams may also be classified according to use or purpose, for example, explanatory and/or how to diagrams. Thousands of diagram techniques exist. Some more examples follow: