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Built-in Mathematica Symbol

Not (!, ¬)

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

Not[expr] can be input in StandardForm and InputForm as ¬expr. The character can be entered as Esc ! Esc, Esc not Esc or \[Not]. »

Not gives symbolic results when necessary, applying various simplification rules to them.

If you are using Mathematica 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. »

Negate assertions:

Symbolic negation:

Enter using Esc not Esc:

Negate assertions:

Symbolic negation:

Enter using Esc not Esc:

Double negation simplifies to the identity:

Negate equations and inequalities:

Negate quantifiers:

Negate conditions in Mathematica code:

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

This shows the set:

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:

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