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The relational algebra uses set union, set difference, and Cartesian product from set theory, and adds additional constraints to these operators to create new ones.. For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes.
Intuitively, if a functional dependency X → Y holds in R, then the relation can be safely split in two relations alongside the column X (which is a key for () ()) ensuring that when the two parts are joined back no data is lost, i.e. a functional dependency provides a simple way to construct a lossless join decomposition of R in two smaller ...
One-to-many often refer to a primary key to foreign key relationship between two tables, where the record in the first table can relate to multiple records in the second table. A foreign key is one side of the relationship that shows a row or multiple rows, with one of those rows being the primary key already listed on the first table.
For example, think of A as Authors, and B as Books. An Author can write several Books, and a Book can be written by several Authors. In a relational database management system, such relationships are usually implemented by means of an associative table (also known as join table, junction table or cross-reference table), say, AB with two one-to-many relationships A → AB and B → AB.
An associative (or junction) table maps two or more tables together by referencing the primary keys (PK) of each data table. In effect, it contains a number of foreign keys (FK), each in a many-to-one relationship from the junction table to the individual data tables. The PK of the associative table is typically composed of the FK columns ...
Conversely, an inner join can result in disastrously slow performance or even a server crash when used in a large volume query in combination with database functions in an SQL Where clause. [2] [3] [4] A function in an SQL Where clause can result in the database ignoring relatively compact table indexes. The database may read and inner join the ...
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A table in a SQL database schema corresponds to a predicate variable; the contents of a table to a relation; key constraints, other constraints, and SQL queries correspond to predicates. However, SQL databases deviate from the relational model in many details , and Codd fiercely argued against deviations that compromise the original principles.