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Adding local short description: "Relational database theory concept", overriding Wikidata description "in relational database theory, a constraint between two sets of attributes in a relation from a database" |
→Example: Made it more concise and clear |
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:''X'' → ''Y'' and ''X'' → ''Z'' [[if and only if]] ''X'' → ''YZ''
== Closure ==
=== Closure of functional dependency === The closure is essentially the full set of values that can be determined from a set of known values for a given relationship using its functional dependencies. One uses [[Armstrong's axioms]] to provide a proof - i.e. reflexivity, augmentation, transitivity.
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=== Closure of a set of attributes ===
Closure of a set of attributes X with respect to <math>F</math> is the set X<sup>+</sup> of all attributes that are functionally determined by X using <math>F</math><sup>+</sup>.
==== Example ====
Imagine the following list of FDs. We are going to calculate a closure for A (written as A<sup>+</sup>) from this relationship.
# ''A'' → ''B''
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| A → ABCD (by (c), and 2)
}}
Therefore, A<sup>+</sup>= ABCD. Because A<sup>+</sup> includes every attribute in the relationship, it is a [[superkey]].
== Covers and equivalence ==
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