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Additionally, because SQL operators return Unknown when comparing anything with Null directly, SQL provides two Null-specific comparison predicates: IS NULL and IS NOT NULL test whether data is or is not Null. [8] SQL does not explicitly support universal quantification, and must work it out as a negated existential quantification.
Conjunctive queries also correspond to select-project-join queries in relational algebra (i.e., relational algebra queries that do not use the operations union or difference) and to select-from-where queries in SQL in which the where-condition uses exclusively conjunctions of atomic equality conditions, i.e. conditions constructed from column ...
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.
Standard SQL uses the same operators as BASIC, while many databases allow != in addition to <> from the standard. SQL follows strict boolean algebra, i.e. doesn't use short-circuit evaluation, which is common to most languages below. E.g. PHP has it, but otherwise it has these same two operators defined as aliases, like many SQL databases.
Basic SQL comparison operators always return Unknown when comparing anything with Null, so the SQL standard provides for two special Null-specific comparison predicates. The IS NULL and IS NOT NULL predicates (which use a postfix syntax) test whether data is, or is not, Null.
Booleans appear in SQL when a condition is needed, such as WHERE clause, in form of predicate which is produced by using operators such as comparison operators, IN operator, IS (NOT) NULL etc. However, apart from TRUE and FALSE, these operators can also yield a third state, called UNKNOWN, when comparison with NULL is made.
Actual SQL implementations normally use other approaches, such as hash joins or sort-merge joins, since computing the Cartesian product is slower and would often require a prohibitively large amount of memory to store. SQL specifies two different syntactical ways to express joins: the "explicit join notation" and the "implicit join notation".
Set operations in SQL is a type of operations which allow the results of multiple queries to be combined into a single result set. [1] Set operators in SQL include UNION, INTERSECT, and EXCEPT, which mathematically correspond to the concepts of union, intersection and set difference.