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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.
An illustration of a compact set K, a compact neighborhood V of K, and an open set U containing V. Date: 9 August 2007, 01:14 (UTC) Source: self-made with Inkscape based on Image:Venn A subset B.svg: Author: Oleg Alexandrov
The following other wikis use this file: Usage on bg.wikipedia.org Кръгове на Ойлер; Usage on bn.wikipedia.org অয়লার রেখাচিত্র
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
English: The necessary and sufficient conditions in the language of sets (Venn diagrams). Necessary condition means that in order to get into the sufficient area, S, you must at first enter the necessary area, N. Sufficient condition means that being in S ensures that you are in the N. Necessary and sufficient (if and only if) condition means that S = N.
A Hasse diagram is a simple picture of a finite partially ordered set, forming a drawing of the partial order's transitive reduction. Concretely, one represents each element of the set as a vertex on the page and draws a line segment or curve that goes upward from x to y precisely when x < y and there is no z such that x < z < y .
[c] For example, Hill & Peterson (1968) [13] present the Venn diagram with shading and all. They give examples of Venn diagrams to solve example switching-circuit problems, but end up with this statement: "For more than three variables, the basic illustrative form of the Venn diagram is inadequate.
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,
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