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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.
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. The points inside a curve labelled S represent elements of the set S, while points outside the boundary represent elements not in the set S.
In the adjacent diagram, examples of small Venn diagrams are transformed into Euler diagrams by sequences of transformations; some of the intermediate diagrams have concurrency of curves. However, this sort of transformation of a Venn diagram with shading into an Euler diagram without shading is not always possible.
File information Description Venn Diagrams Representing all Intersectional Logic Gates Between Two Inputs. Based on Image:LogicGates.jpg.. Source I (ZanderSchubert ()) created this work entirely by myself.
The three Venn diagrams in the figure below represent respectively conjunction x ∧ y, disjunction x ∨ y, and complement ¬x. Figure 2. Venn diagrams for conjunction, disjunction, and complement. For conjunction, the region inside both circles is shaded to indicate that x ∧ y is 1 when both variables are 1.
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.
De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
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,