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Nand[e1,e2,…]

is the logical NAND function. It evaluates its arguments in order, giving True immediately if any of them are False, and False if they are all True.

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Nand

Nand[e1,e2,…]

is the logical NAND function. It evaluates its arguments in order, giving True immediately if any of them are False, and False if they are all True.

Details

  • Nand[e1,e2,…] can be input in StandardForm and InputForm as e_(1) nand e_(2) nand .... The character ⊼ can be entered as nand or \[Nand]. »
  • Nand[e1,e2,…] is equivalent to Not[And[e1,e2,…]]. »
  • Nand has attribute HoldAll, and explicitly controls the evaluation of its arguments. In Nand[e1,e2,…] the e_(i) are evaluated in order, stopping if any one of them is found to be False. »
  • Nand gives symbolic results when necessary, removing initial arguments that are True. »
  • Nand is not Flat.

Examples

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Basic Examples  (2)

Symbolic arguments:

Wolfram Language code: Nand[x, y, z]

Enter using nand:

Wolfram Language code: p⊼q

Scope  (4)

Nand with explicit True or False arguments will simplify:

Wolfram Language code: Nand[x, True, z]
Wolfram Language code: Nand[x, False, z]

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

Wolfram Language code: Nand[Print[1];False, Print[2];True]
Wolfram Language code: Nand[Print[1];True, Print[2];True]

Symbolic transformations may not preserve argument ordering or Nand operations:

Wolfram Language code: z⊼!x⊼!y
Wolfram Language code: Simplify[%]

TraditionalForm formatting:

Wolfram Language code: Nand[x, y, z]//TraditionalForm

Applications  (4)

Find the Nand of two regions:

Wolfram Language code: RegionPlot[Nand[x ^ 2 + y ^ 2 < 1, x + y > 0], {x, -2, 2}, {y, -2, 2}]

A cellular automaton based on Nand:

Wolfram Language code: ArrayPlot[Boole[CellularAutomaton[{Nand@@#&, {}}, RandomChoice[{True, False}, 40], 20]]]

Simplify trees involving Nand:

Wolfram Language code: NestList[Nand[#, #]&, p, 4]
Wolfram Language code: Simplify[%]

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

Wolfram Language code: Integrate[Boole[Nand[x ^ 2 + y ^ 2 < 1, (x - 1) ^ 2 + y ^ 2 < 2]], {x, -3 / 2, 5 / 2}, {y, -2, 2}]

This shows the set:

Wolfram Language code: RegionPlot[Nand[x ^ 2 + y ^ 2 < 1, (x - 1) ^ 2 + y ^ 2 < 2], {x, -3 / 2, 5 / 2}, {y, -2, 2}]

Properties & Relations  (6)

Truth table for binary Nand:

Wolfram Language code: BooleanTable[{x, y, Nand[x, y]}, {x, y}]//Grid

Ternary Nand:

Wolfram Language code: BooleanTable[{x, y, z, Nand[x, y, z]}, {x, y, z}]//Grid

Zero-argument Nand is False:

Wolfram Language code: Nand[]

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

Wolfram Language code: Nand[2 + 2]

Use BooleanConvert to expand in terms of Or and Not:

Wolfram Language code: BooleanConvert[Nand[p, q, r]]

The negation of Nand is equivalent to And:

Wolfram Language code: BooleanConvert[!Nand[p, q, r]]

Nand of conditions in Boole functions:

Wolfram Language code: Boole[Nand[a, b, c]] - (1 - Boole[a]Boole[b]Boole[c])
Wolfram Language code: Simplify[%]
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_2026_nand, author="Wolfram Research", title="{Nand}", year="2000", howpublished="\url{https://reference.wolfram.com/language/ref/Nand.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_nand, organization={Wolfram Research}, title={Nand}, year={2000}, url={https://reference.wolfram.com/language/ref/Nand.html}, note=[Accessed: 13-June-2026]}