Math 2.0

Mathematical logic and foundations Definition

Conjunctive normal form

Builds on Disjunctive normal form

Definition

A formula of propositional logic is in conjunctive normal form if it is a conjunction of one or more disjunctions of one or more literals. Each disjunction is a clause.

Remarks

Example: (p∨¬q)∧(q∨r)∧¬p(p \vee \neg q) \wedge (q \vee r) \wedge \neg p is in conjunctive normal form. Every formula is logically equivalent to a formula in conjunctive normal form. Negate the formula, put the negation in disjunctive normal form, and use the De Morgan laws. The satisfiability problem for formulas in conjunctive normal form with clauses of 33 literals is NP-complete.

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Disjunctive normal form, definition, no evidence levelDisjunctive normal fo…definitionConjunctive normal form, definition, no evidence levelConjunctive normal fo…definition
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Further reading

  1. Web https://en.wikipedia.org/wiki/Conjunctive_normal_form, Definition
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