Functional Dependency (Relational Algebra)

relational-algebra

Definition

Functional Dependency (Relational Algebra)

Let be a schema of a relation and (subsets of attributes of ).

A functional dependency holds on iff for all legal tuples of the following holds:

Thus, the -values uniquely identify the -values. In other words: The -values determine the -values functionally.

Trivial

Definition

Trivial Functional Dependency (Relational Algebra)

A functional dependency is called trivial iff .

Example: is trivial. See Armstrong’s axioms.

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Set Equivalence

Two sets of functional dependencies and are equivalent if their closures equal: