Search results
Results from the WOW.Com Content Network
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.
In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation.The motivating example of a relation algebra is the algebra 2 X 2 of all binary relations on a set X, that is, subsets of the cartesian square X 2, with R•S interpreted as the usual composition of binary relations R and S, and with the ...
A relation R is called intransitive if it is not transitive, that is, if xRy and yRz, but not xRz, for some x, y, z. In contrast, a relation R is called antitransitive if xRy and yRz always implies that xRz does not hold. For example, the relation defined by xRy if xy is an even number is intransitive, [13] but not antitransitive. [14]
In languages such as C, relational operators return the integers 0 or 1, where 0 stands for false and any non-zero value stands for true. An expression created using a relational operator forms what is termed a relational expression or a condition. Relational operators can be seen as special cases of logical predicates.
The relation "≥" between real numbers is reflexive and transitive, but not symmetric. For example, 7 ≥ 5 but not 5 ≥ 7. The relation "has a common factor greater than 1 with" between natural numbers greater than 1, is reflexive and symmetric, but not transitive. For example, the natural numbers 2 and 6 have a common factor greater than 1 ...
Functional and not injective. For example, the red relation in the diagram is many-to-one, but the green, blue and black ones are not. Many-to-many [d] Not injective nor functional. For example, the black relation in the diagram is many-to-many, but the red, green and blue ones are not. Uniqueness and totality properties: A function [d]
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.
The zero-degree relations represent true and false in relational algebra. [ 1 ] :57 Under the closed-world assumption , an n -ary relation is interpreted as the extension of some n -adic predicate : all and only those n -tuples whose values, substituted for corresponding free variables in the predicate, yield propositions that hold true, appear ...