# Conjunctive normal form

From Encyclopedia of Mathematics

A propositional formula of the form

(*) |

where each , ; , is either an atomic formula (a variable or constant) or the negation of an atomic formula. The conjunctive normal form (*) is a tautology if and only if for any one can find both formulas and among the , for some atomic formula . Given any propositional formula , one can construct a conjunctive normal form equivalent to it and containing the same variables and constants as . This is called the conjunctive normal form of .

#### Comments

The dual of a conjunctive normal form is a disjunctive normal form. Both are also used in the theory of Boolean functions (cf. Boolean functions, normal forms of).

**How to Cite This Entry:**

Conjunctive normal form. S.K. Sobolev (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Conjunctive_normal_form&oldid=13117

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098