represents the k^(th) minterm in n variables.


represents the disjunction of the minterms ki.


represents the disjunction of minterms given by the exponent vectors ui, vi, .


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


gives the Boolean expression in the form specified by form.


  • BooleanMinterms[{{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.
  • 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.


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Basic 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:

Wolfram Research (2008), BooleanMinterms, Wolfram Language function,


Wolfram Research (2008), BooleanMinterms, Wolfram Language function,


Wolfram Language. 2008. "BooleanMinterms." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2008). BooleanMinterms. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_booleanminterms, author="Wolfram Research", title="{BooleanMinterms}", year="2008", howpublished="\url{}", note=[Accessed: 12-July-2024 ]}


@online{reference.wolfram_2024_booleanminterms, organization={Wolfram Research}, title={BooleanMinterms}, year={2008}, url={}, note=[Accessed: 12-July-2024 ]}