# 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

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## Basic Examples(1)

Expand out logic expressions:

## Scope(7)

Represent logic expressions as a disjunction of conjunctions (disjunctive normal form):

Simplify logic expressions:

Expand logic expressions out to forms involving only And, Or, and Not:

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 of Element statements:

## Applications(1)

Prove tautologies:

## Properties & Relations(2)

The output of LogicalExpand is equivalent to the input:

De Morgan's laws:

## Neat Examples(1)

An expanded Xor of variables will always contain terms:

Wolfram Research (1988), LogicalExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/LogicalExpand.html.

#### 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_2022_logicalexpand, author="Wolfram Research", title="{LogicalExpand}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/LogicalExpand.html}", note=[Accessed: 08-June-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_logicalexpand, organization={Wolfram Research}, title={LogicalExpand}, year={1988}, url={https://reference.wolfram.com/language/ref/LogicalExpand.html}, note=[Accessed: 08-June-2023 ]}