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 textbased 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:

Introduced in 1988
 (1.0)
 |
Updated in 1996
 (3.0)