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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 .
A Venn diagram is a representation of mathematical sets: a mathematical diagram representing sets as circles, with their relationships to each other expressed through their overlapping positions, so that all possible relationships between the sets are shown. [4] The Venn diagram is constructed with a collection of simple closed curves drawn in ...
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
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 represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. [3] Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language.
By definition, the empty set is a subset of all sets. From this fact it follows that, according to this mathematical convention, if there are no A 's, then the statements "All A is B " and "No A is B " are always true whereas the statements "Some A is B " and "Some A is not B " are always false.
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.