

UnateQ
Details

- A positive unate Boolean function is also known as a Boolean increasing function.
- A negative unate Boolean function is also known as a Boolean decreasing function.
- The Boolean expression bexpr is positive unate in the variable xi if Boole[bexpr/.xi->False]≤Boole[bexpr/.xi->True] for all values of other variables.
- The Boolean expression bexpr is negative unate in the variable xi if Boole[bexpr/.xi->False]≥Boole[bexpr/.xi->True] for all values of other variables.
- Any combination of variables and their negation can be used.
- UnateQ[bf,{ind1,ind2,…}] tests whether the Boolean function bf is unate in variable k according to the indicator indk.
- The indicators indk can take the following values:
-
True,1 test for positive unate False,0 test for negative unate _ do not test for unateness
Examples
open all close allBasic Examples (2)
Scope (5)
Test for unateness in one variable:
Test for positive unate in one variable, negative unate in another:
Check for unateness of a pure function:
Test for negative unateness in the first variable and positive unateness in the second:
Test for whether a function is positive unate in its first and last variables:
Applications (2)
Enumerate all unate functions of three variables:
ReliabilityDistribution only takes positive unate functions:

Find out which variables are not positive unate:
Remove x4 by setting it to False:
Properties & Relations (6)
Basic positive unate functions:
Basic negative unate functions:
Implies is negative unate in one variable and positive unate in the other:
Some Boolean functions are not unate in any variable:
The fraction of Boolean functions that are positive unate for dimension :
Combinations of positive unate functions are unate:
Combinations of negative unate functions are not necessarily negative unate:
The negation of a positive unate function is negative unate:
Related Guides
History
Text
Wolfram Research (2012), UnateQ, Wolfram Language function, https://reference.wolfram.com/language/ref/UnateQ.html.
CMS
Wolfram Language. 2012. "UnateQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/UnateQ.html.
APA
Wolfram Language. (2012). UnateQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UnateQ.html
BibTeX
@misc{reference.wolfram_2025_unateq, author="Wolfram Research", title="{UnateQ}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/UnateQ.html}", note=[Accessed: 15-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_unateq, organization={Wolfram Research}, title={UnateQ}, year={2012}, url={https://reference.wolfram.com/language/ref/UnateQ.html}, note=[Accessed: 15-August-2025]}