LogicalExpand[expr]
expands out logical combinations of equations, inequalities, and other functions.
LogicalExpand
LogicalExpand[expr]
expands out logical combinations of equations, inequalities, and other functions.
Details and Options
- LogicalExpand applies distributive laws for logical operations.
- LogicalExpand generates ORs of ANDs corresponding to disjunctive normal form, with some contractions.
Examples
open allclose allScope (7)
Represent logic expressions as a disjunction of conjunctions (disjunctive normal form):
Expand logic expressions out to forms involving onlyAnd,Or, andNot:
Expand out combinations of equations:
Get separate equations for different terms in a series:
Convert multi-argument equations and inequalities to two-argument form:
Expand negations ofElement statements:
Properties & Relations (2)
Neat Examples (1)
An expandedXor of
variables will always contain
terms:
See Also
Expand PiecewiseExpand Reduce BooleanConvert Implies Resolve And Not Or
History
Introduced in 1988(1.0)
Text
Wolfram Research (1988), LogicalExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/LogicalExpand.html.
CMS
Wolfram Language. 1988. "LogicalExpand." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LogicalExpand.html.
APA
Wolfram Language. (1988). LogicalExpand. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LogicalExpand.html
BibTeX
@misc{reference.wolfram_2025_logicalexpand, author="Wolfram Research", title="{LogicalExpand}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/LogicalExpand.html}", note=[Accessed: 29-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_logicalexpand, organization={Wolfram Research}, title={LogicalExpand}, year={1988}, url={https://reference.wolfram.com/language/ref/LogicalExpand.html}, note=[Accessed: 29-November-2025]}
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