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Nor
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Nor

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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

open allclose all

Basic Examples  (2)Summary of the most common use cases

In[1]:=1
✖
https://wolfram.com/xid/02cyk-c8c20l
Out[1]=1

Enter using nor:

In[1]:=1
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https://wolfram.com/xid/02cyk-cyw7h8
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/02cyk-ef5l5v

Scope  (4)Survey of the scope of standard use cases

Nor with explicit True or False arguments will simplify:

In[1]:=1
✖
https://wolfram.com/xid/02cyk-i4iqla
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/02cyk-j63r74
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/02cyk-dmd6x9
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/02cyk-dltf5i
Out[2]=2

Symbolic transformations may not preserve argument ordering or Nor operations:

In[1]:=1
✖
https://wolfram.com/xid/02cyk-k00ay
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/02cyk-c40ywc
Out[2]=2

TraditionalForm formatting:

In[1]:=1
✖
https://wolfram.com/xid/02cyk-fzbn0j

Applications  (4)Sample problems that can be solved with this function

Find the Nor of two regions:

In[1]:=1
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https://wolfram.com/xid/02cyk-p4rn8i
Out[1]=1

A cellular automaton based on Nor:

In[1]:=1
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https://wolfram.com/xid/02cyk-x5qd7
Out[1]=1

Simplify trees involving Nor:

In[1]:=1
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https://wolfram.com/xid/02cyk-fo16s3
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/02cyk-dxrg5z
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/02cyk-fe4ca9
Out[1]=1

This shows the set:

In[2]:=2
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https://wolfram.com/xid/02cyk-c14dt7
Out[2]=2

Properties & Relations  (6)Properties of the function, and connections to other functions

Truth table for binary Nor:

In[1]:=1
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https://wolfram.com/xid/02cyk-ib02ro
Out[1]=1

Ternary Nor:

In[3]:=3
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https://wolfram.com/xid/02cyk-cwl4xo
Out[3]=3

Zero-argument Nor is True:

In[1]:=1
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https://wolfram.com/xid/02cyk-9ob000
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/02cyk-g7dcos
Out[1]=1

Use BooleanConvert to expand in terms of And and Not:

In[1]:=1
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https://wolfram.com/xid/02cyk-cz4euq
Out[1]=1

The negation of Nor is equivalent to Or:

In[1]:=1
✖
https://wolfram.com/xid/02cyk-ekebtz
Out[1]=1

Nor of conditions in Boole functions:

In[1]:=1
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https://wolfram.com/xid/02cyk-jec7qu
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/02cyk-yhneo
Out[2]=2
Wolfram Research (2000), Nor, Wolfram Language function, https://reference.wolfram.com/language/ref/Nor.html.
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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.

✖
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.

✖
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

✖
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-April-2025 ]}

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@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-April-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-April-2025 ]}

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