# Disjunctive normal form

From Encyclopedia of Mathematics

A propositional formula of the form

(*) |

where each (; ) is either a variable or the negation of a variable. The form (*) is realizable if and only if, for each , do not contain both the formulas and , where is any variable. For any propositional formula it is possible to construct an equivalent disjunctive normal form containing the same variables as . Such a formula is then said to be the disjunctive normal form of the formula .

**How to Cite This Entry:**

Disjunctive normal form.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Disjunctive_normal_form&oldid=14566

This article was adapted from an original article by S.K. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article