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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.
A relation algebra (L, ∧, ∨, −, 0, 1, •, I, ˘) is an algebraic structure equipped with the Boolean operations of conjunction x∧y, disjunction x∨y, and negation x −, the Boolean constants 0 and 1, the relational operations of composition x•y and converse x˘, and the relational constant I, such that these operations and constants satisfy certain equations constituting an ...
Conjunctive queries without distinguished variables are called boolean conjunctive queries.Conjunctive queries where all variables are distinguished (and no variables are bound) are called equi-join queries, [1] because they are the equivalent, in the relational calculus, of the equi-join queries in the relational algebra (when selecting all columns of the result).
Another form of composition of relations, which applies to general -place relations for , is the join operation of relational algebra. The usual composition of two binary relations as defined here can be obtained by taking their join, leading to a ternary relation, followed by a projection that removes the middle component.
For example, "is a blood relative of" is a symmetric relation, because x is a blood relative of y if and only if y is a blood relative of x. Antisymmetric for all x, y ∈ X, if xRy and yRx then x = y. For example, ≥ is an antisymmetric relation; so is >, but vacuously (the condition in the definition is always false). [11] Asymmetric
The above table is also a simple example of a relational database, a field with theory rooted in relational algebra and applications in data management. [6] Computer scientists, logicians, and mathematicians, however, tend to have different conceptions what a general relation is, and what it is consisted of.
In relational algebra, a selection (sometimes called a restriction to avoid confusion with SQL's use of SELECT) is a unary operation written as or () where: a {\displaystyle a} and b {\displaystyle b} are attribute names,
Mutation and Selection. In relational algebra, a selection (sometimes called a restriction in reference to E.F. Codd's 1970 paper [1] and not, contrary to a popular belief, to avoid confusion with SQL's use of SELECT, since Codd's article predates the existence of SQL) is a unary operation that denotes a subset of a relation.
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