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- Disjunctive_normal_form abstract "In boolean logic, a disjunctive normal form (DNF) is a standardization (or normalization) of a logical formula which is a disjunction of conjunctive clauses; otherwise put, it is an OR of ANDs also known as a Sum of products. As a normal form, it is useful in automated theorem proving. A logical formula is considered to be in DNF if and only if it is a disjunction of one or more conjunctions of one or more literals. A DNF formula is in full disjunctive normal form if each of its variables appears exactly once in every clause. As in conjunctive normal form (CNF), the only propositional operators in DNF are and, or, and not. The not operator can only be used as part of a literal, which means that it can only precede a propositional variable. For example, all of the following formulas are in DNF:However, the following formulas are NOT in DNF:— NOT is the outermost operator— an OR is nested within an ANDConverting a formula to DNF involves using logical equivalences, such as the double negative elimination, De Morgan's laws, and the distributive law.All logical formulas can be converted into disjunctive normal form.However, in some cases conversion to DNF can lead to an exponential explosion of the formula. For example, in DNF, logical formulas of the following form have 2n terms:Any particular Boolean function can be represented by one and only one full disjunctive normal form, one of the two canonical forms.The following is a formal grammar for DNF: disjunct → conjunct disjunct → disjunct ∨ conjunct conjunct → literal conjunct → (conjunct ∧ literal) literal → variable literal → ¬variableWhere variable is any variable.".
- Disjunctive_normal_form wikiPageExternalLink applet.php.
- Disjunctive_normal_form wikiPageID "73341".
- Disjunctive_normal_form wikiPageRevisionID "597060144".
- Disjunctive_normal_form hasPhotoCollection Disjunctive_normal_form.
- Disjunctive_normal_form id "p/d033300".
- Disjunctive_normal_form title "Disjunctive normal form".
- Disjunctive_normal_form subject Category:Normal_forms_(logic).
- Disjunctive_normal_form comment "In boolean logic, a disjunctive normal form (DNF) is a standardization (or normalization) of a logical formula which is a disjunction of conjunctive clauses; otherwise put, it is an OR of ANDs also known as a Sum of products. As a normal form, it is useful in automated theorem proving. A logical formula is considered to be in DNF if and only if it is a disjunction of one or more conjunctions of one or more literals.".
- Disjunctive_normal_form label "Disjunctieve normaalvorm".
- Disjunctive_normal_form label "Disjunctive normal form".
- Disjunctive_normal_form label "Disjunktive Normalform".
- Disjunctive_normal_form label "Dysjunkcyjna postać normalna".
- Disjunctive_normal_form label "Forma normal disjuntiva".
- Disjunctive_normal_form label "Forma normal disyuntiva".
- Disjunctive_normal_form label "Forma normale disgiuntiva".
- Disjunctive_normal_form label "Forme normale disjonctive".
- Disjunctive_normal_form label "Дизъюнктивная нормальная форма".
- Disjunctive_normal_form label "析取范式".
- Disjunctive_normal_form label "選言標準形".
- Disjunctive_normal_form sameAs Disjunktivní_normální_forma.
- Disjunctive_normal_form sameAs Disjunktive_Normalform.
- Disjunctive_normal_form sameAs Forma_normal_disyuntiva.
- Disjunctive_normal_form sameAs Forme_normale_disjonctive.
- Disjunctive_normal_form sameAs Forma_normale_disgiuntiva.
- Disjunctive_normal_form sameAs 選言標準形.
- Disjunctive_normal_form sameAs Disjunctieve_normaalvorm.
- Disjunctive_normal_form sameAs Dysjunkcyjna_postać_normalna.
- Disjunctive_normal_form sameAs Forma_normal_disjuntiva.
- Disjunctive_normal_form sameAs m.0jpw_.
- Disjunctive_normal_form sameAs Q903789.
- Disjunctive_normal_form sameAs Q903789.
- Disjunctive_normal_form wasDerivedFrom Disjunctive_normal_form?oldid=597060144.
- Disjunctive_normal_form isPrimaryTopicOf Disjunctive_normal_form.