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De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
De Morgan's laws; Transposition; Material implication ... Import-export is a name given to the statement as a theorem or truth-functional tautology of propositional ...
Rules of replacement are used in propositional logic to manipulate propositions. Common rules of replacement include de Morgan's laws, commutation, association, distribution, double negation, [a] transposition, material implication, logical equivalence, exportation, and tautology.
De Morgan's laws: In propositional logic and Boolean algebra, De Morgan's laws, [15] [16] [17] also known as De Morgan's theorem, [18] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician.
In classical logic each propositional formula can be converted to an equivalent formula that is in CNF. [1] This transformation is based on rules about logical equivalences: double negation elimination, De Morgan's laws, and the distributive law.
Existential introduction (∃I) concludes that, if the propositional function is known to be true for a particular element of the domain of discourse, then it must be true that there exists an element for which the proposition function is true. Symbolically,
Modus ponendo tollens (MPT; [1] Latin: "mode that denies by affirming") [2] is a valid rule of inference for propositional logic. ... De Morgan's laws (1) 4
In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not-or and that either form can replace the other in logical proofs.