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The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that
In linguistics, negative raising is a phenomenon that concerns the raising of negation from the embedded or subordinate clause of certain predicates to the matrix or main clause. [1] The higher copy of the negation, in the matrix clause, is pronounced; but the semantic meaning is interpreted as though it were present in the embedded clause. [2]
Negation elimination states that anything follows from an absurdity. Sometimes negation elimination is formulated using a primitive absurdity sign . In this case the rule says that from and follows an absurdity. Together with double negation elimination one may infer our originally formulated rule, namely that anything follows from an absurdity.
The exclusive or is also equivalent to the negation of a logical biconditional, by the rules of material implication (a material conditional is equivalent to the disjunction of the negation of its antecedent and its consequence) and material equivalence. In summary, we have, in mathematical and in engineering notation:
Negation flips downward entailing and upward entailing statements within the scope of the negation. For example, changing "one could have seen anything" to "no one could have seen anything" changes the meaning of the last word from "anything" to "nothing".
A propositional logic formula, also called Boolean expression, is built from variables, operators AND (conjunction, also denoted by ∧), OR (disjunction, ∨), NOT (negation, ¬), and parentheses. A formula is said to be satisfiable if it can be made TRUE by assigning appropriate logical values (i.e. TRUE, FALSE) to its variables.
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If a statement's inverse is false, then its converse is false (and vice versa). If a statement's negation is false, then the statement is true (and vice versa). If a statement (or its contrapositive) and the inverse (or the converse) are both true or both false, then it is known as a logical biconditional.