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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.
In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets and is . The symmetric difference of the sets A and B is commonly denoted by (alternatively, ), , or .
Mutual information is a measure of the inherent dependence expressed in the joint distribution of and relative to the marginal distribution of and under the assumption of independence. Mutual information therefore measures dependence in the following sense: if and only if and are independent random variables.
The conditional mutual information is used to inductively define the interaction information, a generalization of mutual information, as follows: where. Because the conditional mutual information can be greater than or less than its unconditional counterpart, the interaction information can be positive, negative, or zero, which makes it hard to ...
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number is equal to itself (reflexive). If , then (symmetric).
A Young diagram or Young tableau, also called Ferrers diagram, is a finite collection of boxes, or cells, arranged in left-justified rows, with the row sizes weakly decreasing (each row has the same or shorter length than its predecessor). Young diagram. Listing the number of boxes in each row gives a partition of a positive integer n, the ...
An example Karnaugh map. This image actually shows two Karnaugh maps: for the function ƒ, using minterms (colored rectangles) and for its complement, using maxterms (gray rectangles). In the image, E () signifies a sum of minterms, denoted in the article as . The Karnaugh map ( KM or K-map) is a method of simplifying Boolean algebra expressions.
Statement. The intersection of and is the set of elements that lie in both set and set . Symbolic statement. In set theory, the intersection of two sets and denoted by [ 1] is the set containing all elements of that also belong to or equivalently, all elements of that also belong to [ 2]