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In SELECT statements SQL returns only results for which the WHERE clause returns a value of True; i.e., it excludes results with values of False and also excludes those whose value is Unknown. Along with True and False, the Unknown resulting from direct comparisons with Null thus brings a fragment of three-valued logic to SQL.
The rules governing SQL three-valued logic are shown in the tables below (p and q represent logical states)" [10] The truth tables SQL uses for AND, OR, and NOT correspond to a common fragment of the Kleene and Łukasiewicz three-valued logic (which differ in their definition of implication, however, SQL defines no such operation).
Logical negation is an operation on one logical value, typically the value of a proposition, that produces a value of true if its operand is false and a value of false if its operand is true. The truth table for NOT p (also written as ¬p , Np , Fpq , or ~p ) is as follows:
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).
The assertion that Q is necessary for P is colloquially equivalent to "P cannot be true unless Q is true" or "if Q is false, then P is false". [9] [1] By contraposition, this is the same thing as "whenever P is true, so is Q". The logical relation between P and Q is expressed as "if P, then Q" and denoted "P ⇒ Q" (P implies Q).
In writing, phrases commonly used as alternatives to P "if and only if" Q include: Q is necessary and sufficient for P, for P it is necessary and sufficient that Q, P is equivalent (or materially equivalent) to Q (compare with material implication), P precisely if Q, P precisely (or exactly) when Q, P exactly in case Q, and P just in case Q. [3]
SQL was initially developed at IBM by Donald D. Chamberlin and Raymond F. Boyce after learning about the relational model from Edgar F. Codd [12] in the early 1970s. [13] This version, initially called SEQUEL (Structured English Query Language), was designed to manipulate and retrieve data stored in IBM's original quasirelational database management system, System R, which a group at IBM San ...
The rule states that P implies Q is logically equivalent to not-or and that either form can replace the other in logical proofs. In other words, if P {\displaystyle P} is true, then Q {\displaystyle Q} must also be true, while if Q {\displaystyle Q} is not true, then P {\displaystyle P} cannot be true either; additionally, when P {\displaystyle ...