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Nand

Nand[e1,e2,…]

is the logical NAND function. It evaluates its arguments in order, givingTrue immediately if any of them areFalse, andFalse if they are allTrue.

Details
Details and OptionsDetails and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
See Also
Tech Notes
Related Guides
Related Links
History
Cite this Page

Nand

Nand[e1,e2,…]

is the logical NAND function. It evaluates its arguments in order, givingTrue immediately if any of them areFalse, andFalse if they are allTrue.

Details

  • Nand[e1,e2,…] can be input inStandardForm andInputForm ase_(1) nand e_(2) nand .... The character⊼ can be entered asnand or\[Nand].»
  • Nand[e1,e2,…] is equivalent toNot[And[e1,e2,…]].»
  • Nand has attributeHoldAll, and explicitly controls the evaluation of its arguments. InNand[e1,e2,…] thee_(i) are evaluated in order, stopping if any one of them is found to beFalse.»
  • Nand gives symbolic results when necessary, removing initial arguments that areTrue.»
  • Nand is notFlat.

Examples

open allclose all

Basic Examples  (2)

Symbolic arguments:

Enter usingnand:

Scope  (4)

Nand with explicitTrue orFalse arguments will simplify:

Nand evaluates its arguments in order, stopping when an argument evaluates toFalse:

Symbolic transformations may not preserve argument ordering orNand operations:

TraditionalForm formatting:

Applications  (4)

Find theNand of two regions:

A cellular automaton based onNand:

Simplify trees involvingNand:

Find the area of the complement of the intersection of sets given by algebraic conditions:

This shows the set:

Properties & Relations  (6)

Truth table for binaryNand:

TernaryNand:

Zero-argumentNand isFalse:

Nand with a single argument will return the negated argument regardless of value:

UseBooleanConvert to expand in terms ofOr andNot:

The negation ofNand is equivalent toAnd:

Nand of conditions inBoole functions:

See Also

BooleanConvert LogicalExpand And Nor Not BooleanCountingFunction

Characters:\[Nand]

Tech Notes

Related Guides

Related Links

History

Introduced in 2000(4.1)

Wolfram Research (2000), Nand, Wolfram Language function, https://reference.wolfram.com/language/ref/Nand.html.

Text

Wolfram Research (2000), Nand, Wolfram Language function, https://reference.wolfram.com/language/ref/Nand.html.

CMS

Wolfram Language. 2000. "Nand." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Nand.html.

APA

Wolfram Language. (2000). Nand. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Nand.html

BibTeX

@misc{reference.wolfram_2025_nand, author="Wolfram Research", title="{Nand}", year="2000", howpublished="\url{https://reference.wolfram.com/language/ref/Nand.html}", note=[Accessed: 29-November-2025]}

BibLaTeX

@online{reference.wolfram_2025_nand, organization={Wolfram Research}, title={Nand}, year={2000}, url={https://reference.wolfram.com/language/ref/Nand.html}, note=[Accessed: 29-November-2025]}

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