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B → C direct dependency relationship exists. Then the functional dependency A → C is a transitive dependency (which follows the axiom of transitivity). In database normalization, one of the important features of third normal form is that it excludes certain types of transitive dependencies.
A database relation (e.g. a database table) is said to meet third normal form standards if all the attributes (e.g. database columns) are functionally dependent on solely a key, except the case of functional dependency whose right hand side is a prime attribute (an attribute which is strictly included into some key).
A set S of functional dependencies is irreducible if the set has the following three properties: Each right set of a functional dependency of S contains only one attribute. Each left set of a functional dependency of S is irreducible. It means that reducing any one attribute from left set will change the content of S (S will lose some information).
An example of such a language is SQL, ... The Book table still has a transitive functional dependency ({Author Nationality} is dependent on {Author}, which is ...
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
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]
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.
In this example, {Manufacturer country} is the functionally dependent attribute which will be removed. Place those partial dependency-dependent attributes (i.e. {Manufacturer country}) in a relation where their corresponding determinant attributes are a candidate key (i.e. {Manufacturer}).