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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  
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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:

Wolfram Language code: !x > 1

Symbolic negation:

Wolfram Language code: !x

Enter using not:

Wolfram Language code: ¬p

Scope  (4)

Double negation simplifies to the identity:

Wolfram Language code: Not[Not[a]]

Negate equations and inequalities:

Wolfram Language code: Not[a == b]
Wolfram Language code: Not[a ≥ b]

Negate quantifiers:

Wolfram Language code: !Exists[x, f[x]]
Wolfram Language code: !ForAll[x, f[x]]

TraditionalForm formatting:

Wolfram Language code: !x//TraditionalForm

Applications  (2)

Negate conditions in Wolfram Language code:

Wolfram Language code: Select[{1, Pi, 2.3, 3 + 7I, x}, !NumberQ[#]&]

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

Wolfram Language code: Integrate[Boole[Not[y ^ 2 - 4x ^ 2 + 4x ^ 4 ≤ 0]], {x, -1, 1}, {y, -1, 1}]

This shows the set:

Wolfram Language code: RegionPlot[Not[y ^ 2 - 4x ^ 2 + 4x ^ 4 ≤ 0], {x, -1, 1}, {y, -1, 1}]

Properties & Relations  (4)

Truth table for Not:

Wolfram Language code: BooleanTable[{x, Not[x]}, {x}]//Grid

Use BooleanConvert to simplify the negation of Implies:

Wolfram Language code: BooleanConvert[!Implies[a, b]]

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

Wolfram Language code: BooleanConvert[!(a && b)]
Wolfram Language code: BooleanConvert[!(a || b || c)]

Negation of the condition for Boole function:

Wolfram Language code: Boole[!a] == 1 - Boole[a]
Wolfram Language code: Simplify[%]

Possible Issues  (1)

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

Wolfram Language code: (!True)
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_2026_not, author="Wolfram Research", title="{Not}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Not.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_not, organization={Wolfram Research}, title={Not}, year={1996}, url={https://reference.wolfram.com/language/ref/Not.html}, note=[Accessed: 12-June-2026]}