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Encyclopedia > Euler diagram
An Euler diagram does not need to show all possible intersections.
Enlarge
An Euler diagram does not need to show all possible intersections.
A Venn diagram shows all possible intersections.
Enlarge
A Venn diagram shows all possible intersections.

An Euler diagram, named after it's inventor Leonhard Euler[1], is similar to a Venn diagram, but does not have to contain all zones (where a zone is defined as the area of intersection of two or more sets). Thus, an Euler diagram can define a universe of discourse, i.e. it can define a system whereby certain intersections are not possible or considered. Image File history File links EulerDiagram. ... Image File history File links EulerDiagram. ... Image File history File links VennDiagram. ... Image File history File links VennDiagram. ... Euler redirects here. ... Venn diagrams are illustrations used in the branch of mathematics known as set theory. ... In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. ... In mathematics, a set can be thought of as any collection of distinct things considered as a whole. ... The term universe of discourse generally refers to the entire set of terms used in a specific discourse, i. ...


Thus, a Venn diagram containing the attributes for Animal, Mineral and FourLegs would have to contain intersections where something was both animal and mineral and had legs. A Venn diagram therefore, shows all possible combinations of conjunctions.


An Euler diagram can be structured so that these nonsensical intersections do not exist, thus defining a universe of discourse for this subject. In other words, the Euler diagram can represent degenerate conjunctions. The term universe of discourse generally refers to the entire set of terms used in a specific discourse, i. ...


A modern extension to Euler diagrams, is the spider diagram, whereby existential points are added to the diagram, which can be linked. This gives the diagrams a disjunctive aspect. The diagrams already have a conjunctive aspect (i.e. a zone defines that the existence of an object in the zone has the attributes 'ANDed' together). The spider diagram thus allows logical OR conditions to be modelled with an Euler diagram. A spider diagram adds existential points to an Euler diagram. ... Existentialism is a philosophical movement emphasizing individualism, individual freedom, and subjectivity. ... OR logic gate. ... AND Logic Gate In logic and mathematics, logical conjunction (usual symbol and) is a two-place logical operation that results in a value of true if both of its operands are true, otherwise a value of false. ... A spider diagram adds existential points to an Euler diagram. ...


See also


  Results from FactBites:
 
Euler Diagrams and Quantified Expressions (942 words)
Euler diagrams, inaccurately referred to as Venn diagrams in your text, were an informal way to convey the ideas that are involved in what was subsequently known as quantification.
Your text provides two alternative Euler diagrams for the statement "All A are B," and claims that this indicates that the statement is ambiguous.
The two alternative Euler diagrams provided in your text for this universally quantified are shown in the figure to the right.
Venn diagram - Wikipedia, the free encyclopedia (954 words)
Euler diagrams are similar, but do not need to show all the relations; in common usage, this distinction is often ignored.
Euler diagrams are similar to Venn Diagrams, but do not need all the possible relations.
Johnston diagrams are used to illustrate statements in propositional logic such as Neither A nor B is true and are a visual way of illustrating truth tables.
  More results at FactBites »


 

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