# Conjunction

Conjunction[expr,{a1,a2,}]

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

# Examples

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## Basic Examples(3)

The conjunction over a set of variables:

Show that a formula is a tautology:

Find the conditions on a for ab to be true for any b:

## Properties & Relations(5)

Conjunction effectively computes the And over all truth values of the listed variables:

Conjunction is typically more efficient and can handle large numbers of variables:

Conjunction effectively eliminates (ForAll) quantifiers for the list of variables:

Use Resolve to eliminate more general combinations of quantifiers:

TautologyQ is Conjunction over all variables:

Use Disjunction to compute Or over a list of variables:

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

Conjunction is repeated And, just as Product is repeated Times:

Represent Conjunction in terms of Product:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2022_conjunction, author="Wolfram Research", title="{Conjunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Conjunction.html}", note=[Accessed: 05-February-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_conjunction, organization={Wolfram Research}, title={Conjunction}, year={2008}, url={https://reference.wolfram.com/language/ref/Conjunction.html}, note=[Accessed: 05-February-2023 ]}