On the right is page 74 from Couturat 1914 wherein he labels the 8 regions of the Venn diagram. To be found in Christian Weise", a book actually written by Johann Christian Lange. The small text to the left erroneously states: "The first employment of circular diagrams in logic improperly ascribed to Euler. The symbolism A, E, I, and O refers to the categorical statements that can occur in a syllogism. History A page from Hamilton's Lectures on Logic. Regions not part of the set are indicated by coloring them black, in contrast to Euler diagrams, where membership in the set is indicated by overlap as well as color. A Venn diagram must contain all 2 n logically possible zones of overlap between its n curves, representing all combinations of inclusion/exclusion of its constituent sets. Venn diagrams are a more restrictive form of Euler diagrams. A curve completely within the interior of another is a subset of it. Two curves that overlap represent sets that intersect, that have common elements the zone inside both curves represents the set of elements common to both sets (the intersection of the sets). Curves that do not overlap represent disjoint sets, which have no elements in common. Each curve divides the plane into two regions or "zones": the interior, which symbolically represents the elements of the set, and the exterior, which represents all elements that are not members of the set. How or whether these shapes overlap demonstrates the relationships between the sets. Since then, they have also been adopted by other curriculum fields such as reading as well as organizations and businesses.Įuler diagrams consist of simple closed shapes in a two-dimensional plane that each depict a set or category. In the United States, both Venn and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement of the 1960s. The first use of "Eulerian circles" is commonly attributed to Swiss mathematician Leonhard Euler (1707–1783).
Unlike Venn diagrams, which show all possible relations between different sets, the Euler diagram shows only relevant relationships. They are similar to another set diagramming technique, Venn diagrams. They are particularly useful for explaining complex hierarchies and overlapping definitions. An Euler diagram illustrating that the set of "animals with four legs" is a subset of "animals", but the set of "minerals" is disjoint (has no members in common) with "animals" An Euler diagram showing the relationships between different Solar System objectsĪn Euler diagram ( / ˈ ɔɪ l ər/, OY-lər) is a diagrammatic means of representing sets and their relationships. For the geometric Euler circle, see Nine-point circle. This article is about Eulerian circles of set theory and logic.
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