BooleanMinterms [k,n]
represents the k^(th) minterm in n variables.
BooleanMinterms [{k1,k2,…},n]
represents the disjunction of the minterms ki.
BooleanMinterms [{{u1,…,un},{v1,…},…}]
represents the disjunction of minterms given by the exponent vectors ui, vi, ….
BooleanMinterms [spec,{a1,a2,…}]
gives the Boolean expression in variables ai corresponding to the minterms function specified by spec.
BooleanMinterms [spec,{a,a2,…},form]
gives the Boolean expression in the form specified by form.
BooleanMinterms
BooleanMinterms [k,n]
represents the k^(th) minterm in n variables.
BooleanMinterms [{k1,k2,…},n]
represents the disjunction of the minterms ki.
BooleanMinterms [{{u1,…,un},{v1,…},…}]
represents the disjunction of minterms given by the exponent vectors ui, vi, ….
BooleanMinterms [spec,{a1,a2,…}]
gives the Boolean expression in variables ai corresponding to the minterms function specified by spec.
BooleanMinterms [spec,{a,a2,…},form]
gives the Boolean expression in the form specified by form.
Details
- BooleanMinterms [{{u1,u2,…}},{a1,a2,…}] gives b1∧b2∧… 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.
- BooleanMinterms [k,n] is equivalent to BooleanMinterms [{IntegerDigits [k,n,2]}].
- BooleanMinterms [spec] gives a Boolean function object that works like Function .
- BooleanMinterms [spec][a1,a2,…] gives an implicit representation equivalent to the explicit Boolean expression BooleanMinterms [spec,{a1,a2,…}].
- BooleanConvert converts BooleanMinterms [spec][vars] to an explicit Boolean expression.
- In BooleanMinterms [spec,{a1,a2,…},form], the possible forms are as given for BooleanConvert .
- BooleanMinterms [spec,{a1,a2,…}] by default gives an expression in DNF.
Examples
open all close allBasic Examples (4)
Equivalent ways of specifying the same minterm:
Specify a disjunction of minterms:
An equivalent way to specify a disjunction of minterms:
Return a BooleanFunction object representing the disjunction of minterms:
Enumerate all minterms of three variables:
Scope (1)
Specify different forms for the result:
Properties & Relations (4)
The indices correspond to positions of True in the default ordering for BooleanTable :
BooleanMinterms can represent any BooleanFunction :
The mapping from minterms to index:
The mapping from index to minterms:
Using bit vectors:
Use Subsets to enumerate all possible Boolean functions using BooleanMinterms :
BooleanMaxterms is related to BooleanMinterms :
Related Guides
History
Text
Wolfram Research (2008), BooleanMinterms, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanMinterms.html.
CMS
Wolfram Language. 2008. "BooleanMinterms." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BooleanMinterms.html.
APA
Wolfram Language. (2008). BooleanMinterms. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanMinterms.html
BibTeX
@misc{reference.wolfram_2025_booleanminterms, author="Wolfram Research", title="{BooleanMinterms}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanMinterms.html}", note=[Accessed: 24-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_booleanminterms, organization={Wolfram Research}, title={BooleanMinterms}, year={2008}, url={https://reference.wolfram.com/language/ref/BooleanMinterms.html}, note=[Accessed: 24-November-2025]}