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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 .
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
Statement. The symmetric difference is the set of elements that are in either set, but not in the intersection. Symbolic statement. A Δ B = ( A ∖ B ) ∪ ( B ∖ A ) {\displaystyle A\,\Delta \,B=\left (A\setminus B\right)\cup \left (B\setminus A\right)} In mathematics, the symmetric difference of two sets, also known as the disjunctive union ...
Fundamentals. The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
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.
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.
alternating, hyperbolic. In mathematics, the Borromean rings[ a ] are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the three is cut or removed. Most commonly, these rings are drawn as three ...