\begin{definition}[Definition:Logical NAND]
'''NAND''' (that is, '''not and'''), is a binary connective, written symbolically as $p \uparrow q$, whose behaviour is as follows:
:$p \uparrow q$
is defined as:
:'''it is not the case that $p$ and $q$ are both true.'''
$p \uparrow q$ is voiced:
:'''$p$ nand $q$'''
\end{definition}