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Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
A multivariate function, multivariable function, or function of several variables is a function that depends on several arguments. Such functions are commonly encountered. For example, the position of a car on a road is a function of the time travelled and its average speed.
The above concept of relation [a] has been generalized to admit relations between members of two different sets (heterogeneous relation, like "lies on" between the set of all points and that of all lines in geometry), relations between three or more sets (finitary relation, like "person x lives in town y at time z "), and relations between ...
Given a scale or ruler, graphs can also be used to read off the value of an unknown variable plotted as a function of a known one, but this can also be done with data presented in tabular form. Graphs of functions are used in mathematics , sciences , engineering , technology , finance , and other areas.
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
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 uses simple closed ...
The function f is injective if and only if each horizontal line intersects the graph at most once. In this case the graph is said to pass the horizontal line test. If any horizontal line intersects the graph more than once, the function fails the horizontal line test and is not injective. [2]
A depends on B and C; B depends on D. Given a set of objects and a transitive relation with (,) modeling a dependency "a depends on b" ("a needs b evaluated first"), the dependency graph is a graph = (,) with the transitive reduction of R.