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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 .
Venn diagram showing the union of sets A and B as everything not in white. In combinatorics, a branch of mathematics, 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
Exclusive or. Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true ...
where S is the sample space. Compare this to the concept of a set of mutually exclusive events. In such a set no more than one event can occur at a given time. (In some forms of mutual exclusion only one event can ever occur.) The set of all possible die rolls is both mutually exclusive and collectively exhaustive (i.e., "MECE"). The events 1 ...
Euler diagram. An Euler diagram (/ ˈɔɪlər /, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramming technique, Venn diagrams.
Set theory. Statement. The intersection of A and B is the set A ∩ B of elements that lie in both set A and set B . Symbolic statement. A ∩ B = {x: x ∈ A and x ∈ B} 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.
UpSet plots are a data visualization method for showing set data with more than three intersecting sets. UpSet shows intersections in a matrix, with the rows of the matrix corresponding to the sets, and the columns to the intersections between these sets (or vice versa). The size of the sets and of the intersections are shown as bar charts.
An illustration of a compact set K, a compact neighborhood V of K, and an open set U containing V. Date: 9 August 2007, 01:14 (UTC) Source: self-made with Inkscape based on Image:Venn A subset B.svg: Author: Oleg Alexandrov
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