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A relational database consists of named relation variables (relvars) for the purposes of updating the database in response to changes in the real world. An update to a single relvar causes the body of the relation assigned to that variable to be replaced by a different set of tuples.
In relational databases, relvar is a term introduced by C. J. Date and Hugh Darwen as an abbreviation for relation variable in their 1995 paper The Third Manifesto, to avoid the confusion sometimes arising from the use of the term "relation", by the inventor of the relational model, E. F. Codd, for a variable to which a relation is assigned as well as for the relation itself.
Codd's theorem states that relational algebra and the domain-independent relational calculus queries, two well-known foundational query languages for the relational model, are precisely equivalent in expressive power. That is, a database query can be formulated in one language if and only if it can be expressed in the other.
An alternate representation of the previous example would be: { , ,, , ′ ′, } In this example, the value of the requested F domain is directly placed in the formula and the C domain variable is re-used in the query for the existence of a department, since it already holds a crew member's ID.
We define headers as finite subsets of C. A relational database schema is defined as a tuple S = (D, R, h) where D is the domain of atomic values (see relational model for more on the notions of domain and atomic value), R is a finite set of relation names, and h : R → 2 C. a function that associates a header with each relation name in R ...
Most relational database designs resolve many-to-many relationships by creating an additional table that contains the PKs from both of the other entity tables – the relationship becomes an entity; the resolution table is then named appropriately and the two FKs are combined to form a PK. The migration of PKs to other tables is the second ...
For example, in the Order relation the attribute Customer ID is a foreign key. A join is the operation that draws on information from several relations at once. By joining relvars from the example above we could query the database for all of the Customers, Orders, and Invoices.
In relational database theory, a functional dependency is the following constraint between two attribute sets in a relation: Given a relation R and attribute sets ,, X is said to functionally determine Y (written X → Y) if each X value is associated with precisely one Y value.