Negation

Let $p$ be a proposition. The negation of $p$, which is denoted by $\neg p$, is the proposition that "it is not the case that $p$".

$$v(\neg A)=\{\begin{array}{ll}0,& \text{if }v(A)=1\\ 1,& \text{if }v(A)=0\end{array}$$

$p$	$\neg p$
T	F
F	T

For example:

• Let $p$ be that “Today is Tuesday”.
• $\neg p$ means “It is not the case that today is Tuesday”.
  • Or otherwise “Today is not Tuesday” or “It is not Tuesday today”.