Nor

Nor[e1,e2,…]

is the logical NOR function. It evaluates its arguments in order, giving False immediately if any of them are True, and True if they are all False.

Details

  • Nor[e1,e2,…] can be input in StandardForm and InputForm as e_(1) nor e_(2) nor .... The character ⊽ can be entered as nor or \[Nor]. »
  • Nor[e1,e2,…] is equivalent to Not[Or[e1,e2,…]]. »
  • Nor has attribute HoldAll, and explicitly controls the evaluation of its arguments. In Nor[e1,e2,…] the e_(i) are evaluated in order, stopping if any one of them is found to be True. »
  • Nor gives symbolic results when necessary, removing initial arguments that are False.
  • Nor is not Flat.

Examples

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Basic Examples  (2)

Enter using nor:

Scope  (4)

Nor with explicit True or False arguments will simplify:

Nor evaluates its arguments in order, stopping when an argument evaluates to True:

Symbolic transformations may not preserve argument ordering or Nor operations:

TraditionalForm formatting:

Applications  (4)

Find the Nor of two regions:

A cellular automaton based on Nor:

Simplify trees involving Nor:

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

This shows the set:

Properties & Relations  (6)

Truth table for binary Nor:

Ternary Nor:

Zero-argument Nor is True:

Nor with a single argument will return the negated argument regardless of value:

Use BooleanConvert to expand in terms of And and Not:

The negation of Nor is equivalent to Or:

Nor of conditions in Boole functions:

Wolfram Research (2000), Nor, Wolfram Language function, https://reference.wolfram.com/language/ref/Nor.html.

Text

Wolfram Research (2000), Nor, Wolfram Language function, https://reference.wolfram.com/language/ref/Nor.html.

CMS

Wolfram Language. 2000. "Nor." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Nor.html.

APA

Wolfram Language. (2000). Nor. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Nor.html

BibTeX

@misc{reference.wolfram_2025_nor, author="Wolfram Research", title="{Nor}", year="2000", howpublished="\url{https://reference.wolfram.com/language/ref/Nor.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_nor, organization={Wolfram Research}, title={Nor}, year={2000}, url={https://reference.wolfram.com/language/ref/Nor.html}, note=[Accessed: 29-March-2025 ]}