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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.
Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article. In terms of a communication channel in which the output Y {\displaystyle Y} is a noisy version of the input X {\displaystyle X} , these relations ...
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:
A data structure diagram is a diagram type that is used to depict the structure of data elements in the data dictionary. The data structure diagram is a graphical alternative to the composition specifications within such data dictionary entries. [1] The data structure diagrams is a predecessor of the entity–relationship model (E–R model
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 set theory the Venn diagrams tell, that there is an element in every red, and there is no element in any black intersection. Negations of the relations in the matrix on the right. In the Venn diagrams the negation exchanges black and red. In set theory the Venn diagrams tell, that there is an element in one of the red intersections.
A circular list can be split into two circular lists, in constant time, by giving the addresses of the last node of each piece. The operation consists in swapping the contents of the link fields of those two nodes. Applying the same operation to any two nodes in two distinct lists joins the two list into one.