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In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving.
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[8] [9] This provides a procedure for converting between conjunctive normal form and disjunctive normal form. [10] Since the Disjunctive Normal Form Theorem shows that every formula of propositional logic is expressible in disjunctive normal form, every formula is also expressible in conjunctive normal form by means of effecting the conversion ...
This template is for articles like Exclusive or. The colors white and red correspond to Venn diagrams like File:Venn0110.svg , as well as other files like File:Variadic logical XOR.svg . {{ 2-ary truth table | 0 | 1 | 1 | 0 |< math > A \oplus B </ math >}}
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Venn diagram, depicting the truth table values as a colouring of regions of the plane; Algebraically, as a propositional formula using rudimentary Boolean functions: Negation normal form, an arbitrary mix of AND and ORs of the arguments and their complements; Disjunctive normal form, as an OR of ANDs of the arguments and their complements
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...