Negation#
Definition: Negation
The negation function is the Boolean operator \(\mathop{\operatorname{NOT}}: \{0, 1\} \to \{0,1\}\) defined in the following way:
\[ \mathop{\operatorname{NOT}} (x) \overset{\text{def}}{=} \begin{cases} 0 \qquad \text{if } x = 1 \\ 1 \qquad \text{if } x = 0 \end{cases} \]
Notation
It is much more common to write \(\mathop{\operatorname{NOT}}(x)\) in one of the following ways:
\[ \neg x \qquad !x \qquad \overline{x} \]