functional dependencies - definition. What is functional dependencies
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IN RELATIONAL DATABASE THEORY, A CONSTRAINT BETWEEN TWO SETS OF ATTRIBUTES IN A RELATION FROM A DATABASE
Fundep; Functional dependencies; Heath's theorem; Functional Dependency

Functional dependency         
In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database. In other words, a functional dependency is a constraint between two attributes in a relation.
functional dependency         
<database> Given a relation R (in a relational database), attribute Y of R is functionally dependent on attribute X of R and X of R functionally determines Y of R (in symbols R.X -> R.Y) if and only if each X in R has associated with it precisely one Y in R (at any one time). Attributes X and Y may be composite. This is very close to a function in the mathematical sense. (1997-09-01)
Federal Dependencies of Venezuela         
  • Mangroves in Federal Dependencies
  • Cayo de Agua, [[Los Roques Archipelago]]
  • Reefs in the Dos Mosquises Islands
  • 600px
  • The Simón Bolívar Scientific-Military Base on the Aves Island established in 1978
  • Beaches of Las Aves Archipelago east of Bonaire and west of Los Roques
  • The Dutch settled in La Tortuga in 1605 until they were again evicted by the Spanish in 1631.
  • La Blanquilla is one of the largest islands in the Federal Dependencies
  • [[La Orchila]] is one of the 3 federal dependencies included in the Francisco de Miranda Insular Territory since 2011.
  • Map showing the maritime border treaties between Venezuela and the US, France, the Netherlands, Dominican Republic and Trinidad and Tobago, setting part of the borders of the Federal Dependencies.
  • Location of the Francisco de Miranda Insular Territory.
  • Dolphins in Los Roques Archipelago National Park
  • Gran Roque Island, One of the most visited islands of the Federal Dependencies
FIRST-LEVEL ADMINISTRATIVE TERRITORIAL ENTITY OF VENEZUELA, NOT ORGANIZED AS A STATE
Venezuelan Federal Dependencies; Dependencias Federales Federal Dependency, Venezuela; Federal Dependencies; Federal dependencies; Venezuelan Islands; Dependencias Federales, Venezuela; Federal dependency; Federal dependencies of venezuela; Federal Dependency; Dependencias Federales; Dependencias Federales (Venezuela); Federal dependencies of Venezuela; Dependencias Federales de Venezuela; Venezuelan Antilles; Economy of Federal Dependencies of Venezuela; The Federal Dependencies of Venezuela
The Federal Dependencies of Venezuela () encompass most of Venezuela's offshore islands in the Caribbean Sea and the Gulf of Venezuela, excluding those islands that form the State of Nueva Esparta and some Caribbean coastal islands that are integrated with nearby states. These islands, with a total area of 342 square kilometres, are sparsely populated – according to the preliminary results of the 2011 Census only 2,155 people live there permanently, with another hundred from Margarita Island who live there seasonally to engage in fishing.

ويكيبيديا

Functional dependency

In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database. In other words, a functional dependency is a constraint between two attributes in a relation. Given a relation R and sets of attributes X , Y R {\displaystyle X,Y\subseteq R} , X is said to functionally determine Y (written XY) if and only if each X value in R is associated with precisely one Y value in R; R is then said to satisfy the functional dependency XY. Equivalently, the projection Π X , Y R {\displaystyle \Pi _{X,Y}R} is a function, i.e. Y is a function of X. In simple words, if the values for the X attributes are known (say they are x), then the values for the Y attributes corresponding to x can be determined by looking them up in any tuple of R containing x. Customarily X is called the determinant set and Y the dependent set. A functional dependency FD: XY is called trivial if Y is a subset of X.

In other words, a dependency FD: XY means that the values of Y are determined by the values of X. Two tuples sharing the same values of X will necessarily have the same values of Y.

The determination of functional dependencies is an important part of designing databases in the relational model, and in database normalization and denormalization. A simple application of functional dependencies is Heath's theorem; it says that a relation R over an attribute set U and satisfying a functional dependency XY can be safely split in two relations having the lossless-join decomposition property, namely into Π X Y ( R ) Π X Z ( R ) = R {\displaystyle \Pi _{XY}(R)\bowtie \Pi _{XZ}(R)=R} where Z = UXY are the rest of the attributes. (Unions of attribute sets are customarily denoted by there juxtapositions in database theory.) An important notion in this context is a candidate key, defined as a minimal set of attributes that functionally determine all of the attributes in a relation. The functional dependencies, along with the attribute domains, are selected so as to generate constraints that would exclude as much data inappropriate to the user domain from the system as possible.

A notion of logical implication is defined for functional dependencies in the following way: a set of functional dependencies Σ {\displaystyle \Sigma } logically implies another set of dependencies Γ {\displaystyle \Gamma } , if any relation R satisfying all dependencies from Σ {\displaystyle \Sigma } also satisfies all dependencies from Γ {\displaystyle \Gamma } ; this is usually written Σ Γ {\displaystyle \Sigma \models \Gamma } . The notion of logical implication for functional dependencies admits a sound and complete finite axiomatization, known as Armstrong's axioms.