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A functional dependency FD: X → Y is called trivial if Y is a subset of X. ... A classic example of functional dependency is the employee department model.
A relational schema R is in Boyce–Codd normal form if and only if for every one of its functional dependencies X → Y, at least one of the following conditions hold: [5] X → Y is a trivial functional dependency (Y ⊆ X), X is a superkey for schema R. [5]
Given a set of functional dependencies , an Armstrong relation is a relation which satisfies all the functional dependencies in the closure + and only those dependencies. . Unfortunately, the minimum-size Armstrong relation for a given set of dependencies can have a size which is an exponential function of the number of attributes in the dependencies conside
Every non-trivial functional dependency begins with a superkey (a stricter form of 3NF) — Every non-trivial multivalued dependency begins with a superkey — Every join dependency has a superkey component [8] — Every join dependency has only superkey components — Every constraint is a consequence of domain constraints and key constraints
To rephrase Zaniolo's definition more simply, the relation is in 3NF if and only if for every non-trivial functional dependency X → Y, X is a superkey or Y \ X consists of prime attributes. Zaniolo's definition gives a clear sense of the difference between 3NF and the more stringent Boyce–Codd normal form (BCNF).
If one of the tables in the join has all the attributes of the table , the join dependency is called trivial. The join dependency plays an important role in the fifth normal form (5NF), also known as project-join normal form, because it can be proven that if a scheme is decomposed in tables to , the decomposition will be a lossless-join ...
A trivial multivalued dependency X Y is one where either Y is a subset of X, or X and Y together form the whole set of attributes of the relation. A functional dependency is a special case of multivalued dependency. In a functional dependency X → Y, every x determines exactly one y, never more than one.
For example, in an employee ... is the trivial superkey. ... A superkey defines a functional dependency constraint of a relation schema which must hold for all ...