Search results
Results from the WOW.Com Content Network
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.
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".
De Morgan's laws commonly apply to text searching using Boolean operators AND, OR, and NOT. Consider a set of documents containing the words "cats" and "dogs". De Morgan's laws hold that these two searches will return the same set of documents: Search A: NOT (cats OR dogs) Search B: (NOT cats) AND (NOT dogs)
Just as arithmetic features binary operations on numbers, set theory features binary operations on sets. [6] The following is a partial list of them: Union of the sets A and B, denoted A ∪ B, is the set of all objects that are a member of A, or B, or both. [7] For example, the union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4}.
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 ...
Three sets involved. [edit] In the left hand sides of the following identities, L{\displaystyle L}is the L eft most set, M{\displaystyle M}is the M iddle set, and R{\displaystyle R}is the R ight most set. Precedence rules. There is no universal agreement on the order of precedenceof the basic set operators.
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