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!expr

is the logical NOT function. It gives False if expr is True, and True if it is False.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Possible Issues  
See Also
Tech Notes
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Not

!expr

is the logical NOT function. It gives False if expr is True, and True if it is False.

Details

  • Not[expr] can be input in StandardForm and InputForm as ¬expr. The character ¬ can be entered as !, not, or ∖[Not]. »
  • Not gives symbolic results when necessary, applying various simplification rules to them.
  • If you are using the Wolfram System with a text‐based front end, then you cannot use the notation !expr for Not[expr] if it appears at the very beginning of a line. In this case, !expr is interpreted as a shell escape. »

Examples

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Basic Examples  (3)

Negate assertions:

Symbolic negation:

Enter using not:

Scope  (4)

Double negation simplifies to the identity:

Negate equations and inequalities:

Negate quantifiers:

TraditionalForm formatting:

Applications  (2)

Negate conditions in Wolfram Language code:

Find the area of the complement of a set given by algebraic conditions:

This shows the set:

Properties & Relations  (4)

Truth table for Not:

Use BooleanConvert to simplify the negation of Implies:

De Morgan's laws relate And, Or, and Not:

Negation of the condition for Boole function:

Possible Issues  (1)

Use parentheses to ensure ! beginning a line is not taken as a shell escape when using a terminal interface:

Wolfram Research (1988), Not, Wolfram Language function, https://reference.wolfram.com/language/ref/Not.html (updated 1996).

Text

Wolfram Research (1988), Not, Wolfram Language function, https://reference.wolfram.com/language/ref/Not.html (updated 1996).

CMS

Wolfram Language. 1988. "Not." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Not.html.

APA

Wolfram Language. (1988). Not. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Not.html

BibTeX

@misc{reference.wolfram_2025_not, author="Wolfram Research", title="{Not}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Not.html}", note=[Accessed: 28-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_not, organization={Wolfram Research}, title={Not}, year={1996}, url={https://reference.wolfram.com/language/ref/Not.html}, note=[Accessed: 28-August-2025]}