# BooleanMaxterms

BooleanMaxterms[k,n]

represents the k maxterm in n variables.

BooleanMaxterms[{k1,k2,},n]

represents the conjunction of the maxterms ki.

BooleanMaxterms[{{u1,,un},{v1,},}]

represents the conjunction of maxterms given by the exponent vectors ui, vi, .

BooleanMaxterms[spec,{a1,a2,}]

gives the Boolean expression in variables ai corresponding to the maxterms function specified by spec.

BooleanMaxterms[spec,{a,a2,},form]

gives the Boolean expression in the form specified by form.

# Details

• BooleanMaxterms[{{u1,u2,}},{a1,a2,}] gives b1b2 where bi==ai if ui is True and bi=¬ai if ui is False.
• The ui etc. can be either True and False or 1 and 0.
• BooleanMaxterms[k,n] is equivalent to BooleanMaxterms[{IntegerDigits[k,n,2]}].
• BooleanMaxterms[spec] gives a Boolean function object that works like Function.
• BooleanMaxterms[spec][a1,a2,] gives an implicit representation equivalent to the explicit Boolean expression BooleanMaxterms[spec,{a1,a2,}].
• BooleanConvert converts BooleanMaxterms[spec][vars] to an explicit Boolean expression.
• In BooleanMaxterms[spec,{a1,a2,},form], the possible forms are as given for BooleanConvert.
• BooleanMaxterms[spec,{a1,a2,}] by default gives an expression in CNF.

# Examples

open allclose all

## Basic Examples(4)

Equivalent ways of specifying the same maxterm:

Specify a conjunction of maxterms:

An equivalent way to specify a conjunction of maxterms:

Return a BooleanFunction object representing the conjunction of maxterms:

Enumerate all maxterms of three variables:

## Scope(1)

Specify different forms for the result:

## Applications(1)

Produce a CNF formula for (1,3,5):

## Properties & Relations(4)

The indices correspond to positions of False, in the default ordering for BooleanTable:

BooleanMaxterms can represent any BooleanFunction:

The mapping from maxterms to index:

The mapping from index to maxterms:

Using bit vectors:

Use Subsets to enumerate all possible Boolean functions using BooleanMaxterms:

BooleanMinterms is related to BooleanMaxterms:

Wolfram Research (2008), BooleanMaxterms, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanMaxterms.html.

#### Text

Wolfram Research (2008), BooleanMaxterms, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanMaxterms.html.

#### CMS

Wolfram Language. 2008. "BooleanMaxterms." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BooleanMaxterms.html.

#### APA

Wolfram Language. (2008). BooleanMaxterms. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanMaxterms.html

#### BibTeX

@misc{reference.wolfram_2024_booleanmaxterms, author="Wolfram Research", title="{BooleanMaxterms}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanMaxterms.html}", note=[Accessed: 29-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_booleanmaxterms, organization={Wolfram Research}, title={BooleanMaxterms}, year={2008}, url={https://reference.wolfram.com/language/ref/BooleanMaxterms.html}, note=[Accessed: 29-May-2024 ]}