Conjunction—Wolfram Language Documentation (original) (raw)

BUILT-IN SYMBOL

• See Also
  • And
  • Disjunction
  • ForAll
  • Resolve
  • Product
  • BooleanConvert
• Related Guides
  • Boolean Computation
  • Graph Programming

Conjunction

Conjunction[expr,{a1,a2,…}]

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

Details

• Conjunction[expr,{a1,a2,…}] effectively applies And to the results of substituting all possible combinations of True and False for the ai in expr.
• Conjunction gives a resolved form of ∀a1,a2,…expr.
• Conjunction is to And what Product is to Times.

Examples

open allclose all

Basic Examples (3)

The conjunction over a set of variables:

Show that a formula is a tautology:

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

Properties & Relations (5)

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_2025_conjunction, author="Wolfram Research", title="{Conjunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Conjunction.html}", note=[Accessed: 30-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_conjunction, organization={Wolfram Research}, title={Conjunction}, year={2008}, url={https://reference.wolfram.com/language/ref/Conjunction.html}, note=[Accessed: 30-April-2025 ]}