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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.
A Hasse diagram is a simple picture of a finite partially ordered set, forming a drawing of the partial order's transitive reduction. Concretely, one represents each element of the set as a vertex on the page and draws a line segment or curve that goes upward from x to y precisely when x < y and there is no z such that x < z < y .
The Venn diagram is a commonly used method to illustrate the relations between sets. The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century.
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 problem, in this context, with informally formulated set theories, not derived from (and implying) any particular axiomatic theory, is that there may be several widely differing formalized versions, that have both different sets and different rules for how new sets may be formed, that all conform to the original informal definition.