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In computer science, a relational operator is a programming language construct or operator that tests or defines some kind of relation between two entities. These include numerical equality ( e.g. , 5 = 5 ) and inequalities ( e.g. , 4 ≥ 3 ).
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.
All comparison operators can be overloaded in C++. Since C++20, the inequality operator is automatically generated if operator== is defined and all four relational operators are automatically generated if operator<=> is defined. [1]
Common examples that differ from functions syntactically are relational operators, e.g. ">" for "greater than", with names often outside the language's set of identifiers for functions, and called with a syntax different from the language's syntax for calling functions.
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 operator distributes over if it both left distributes and right distributes over . In the definitions above, to transform one side to the other, the innermost operator (the operator inside the parentheses) becomes the outermost operator and the outermost operator becomes the innermost operator.
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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 ...