# Disjunction

Disjunction[expr,{a1,a2,}]

gives the disjunction of expr over all choices of the Boolean variables ai.

# Examples

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## Basic Examples(3)

The disjunction over a set of variables:

Check whether an expression is satisfiable:

Find the conditions on a for ab to be satisfiable:

## Properties & Relations(5)

Disjunction effectively computes the Or over all truth values of the listed variables:

Disjunction is typically more efficient and can work large numbers of variables:

Disjunction eliminates (Exists) quantifiers for the list of variables:

Use Resolve to eliminate more general combinations of quantifiers:

SatisfiableQ is Disjunction over all variables:

Use Conjunction to compute And over a list of variables:

Conjunction is related to Disjunction by de Morgan's law:

Disjunction is effectively repeated Or, just as Sum is repeated Plus:

Represent Disjunction in terms of Sum:

Wolfram Research (2008), Disjunction, Wolfram Language function, https://reference.wolfram.com/language/ref/Disjunction.html.

#### Text

Wolfram Research (2008), Disjunction, Wolfram Language function, https://reference.wolfram.com/language/ref/Disjunction.html.

#### CMS

Wolfram Language. 2008. "Disjunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Disjunction.html.

#### APA

Wolfram Language. (2008). Disjunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Disjunction.html

#### BibTeX

@misc{reference.wolfram_2022_disjunction, author="Wolfram Research", title="{Disjunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Disjunction.html}", note=[Accessed: 08-June-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_disjunction, organization={Wolfram Research}, title={Disjunction}, year={2008}, url={https://reference.wolfram.com/language/ref/Disjunction.html}, note=[Accessed: 08-June-2023 ]}