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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.
Composite of two pages from Venn (1881a), pp. 115–116 showing his example of how to convert a syllogism of three parts into his type of diagram; Venn calls the circles "Eulerian circles" [10] But nevertheless, he contended, "the inapplicability of this scheme for the purposes of a really general logic" [ 9 ] (p 100) and then noted that,
A Venn diagram is a representation of mathematical sets: a mathematical diagram representing sets as circles, with their relationships to each other expressed through their overlapping positions, so that all possible relationships between the sets are shown.
The commonly-used diagram for the Borromean rings consists of three equal circles centered at the points of an equilateral triangle, close enough together that their interiors have a common intersection (such as in a Venn diagram or the three circles used to define the Reuleaux triangle).
Venn diagram showing the union of sets A and B as everything not in white. In combinatorics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as
Venn diagram of = . The symmetric difference is equivalent to the union of both relative complements, that is: [1] = (), The symmetric difference can also be expressed using the XOR operation ⊕ on the predicates describing the two sets in set-builder notation:
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
Euler circle may refer to: Nine-point circle, a circle that can be constructed for any given triangle; Euler diagram, a diagrammatic means of representing propositions and their relationships; Venn diagram, a diagram type originally also called Euler circle