Disjunctive Normal Form


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Disjunctive Normal Form

(DNF) A logical formula consisting of a disjunction of conjunctions where no conjunction contains a disjunction. E.g. the DNF of (A or B) and C is (A and C) or (B and C).
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All boolean expressions can be expressed in disjunctive normal form, thus, the expression B(M) can be transformed into [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] We introduce a new vertex value [lambda] which is the adjacent vertex of each graph vertex by default.
Any propositional formulae has an equivalent disjunctive normal form and an equivalent conjunctive normal form.
Definition 2: A disjunctive normal form of a Boolean function is a developed disjunctive normal form is any variable appears once and only once in any clause, either in negative form or not (never under both forms) [11];
It is observed that the transformation from a disjunctive normal form to a developed disjunctive normal form is done very easily by replacing clause 0 from the disjunctive normal form that does not contain a key [k.
We are looking to transform this query in a developed disjunctive normal form, i.
A classically valid sequent of truth-functional logic is expressible as a sequent with a formula in conjunctive normal form as premise and one in disjunctive normal form as conclusion, thus (ibid.
For a language generated by any finite number of propositional variables there is an easy algorithm for obtaining the sentence [Delta]X in disjunctive normal form, given the truth table of a sentence X.
It is not too difficult to show that if X is a non-contradictory sentence in disjunctive normal form, then [Delta]X may be obtained as the result of performing the following simple operation on X: replace by T all [not p.
For a non-contradictory sentence in disjunctive normal form one may obtain [Nabla]X by simply replacing all unnegated occurrences of propositional symbols [p.