\begin{definition}[Definition:Conditional/Truth Table/Number]
The truth table number of the conjunction operator $p \land q$ is as follows:
Ascending order:
:$1101$ or $\T \T \F \T$
Descending order:
:$1011$ or $\T \F \T \T$
As $\implies$ is not commutative, it is also instructive to give a truth table number for $p \impliedby q$ (which of course is the same as $q \implies p$).
Hence the truth table numbers of the conditional (implication) operator $p \impliedby q$ and the complements of both $p \implies q$ and $p \impliedby q$ are as follows:
$p \impliedby q$:
Ascending order:
:$1011$ or $\T \F \T \T$
Descending order:
:$1101$ or $\T \T \F \T$
$\map \neg {p \implies q}$:
Ascending order:
:$0010$ or $\F \F \T \F$
Descending order:
:$0100$ or $\F \T \F \F$
$\map \neg {q \implies p}$:
Ascending order:
:$0100$ or $\F \T \F \F$
Descending order:
:$0010$ or $\F \F \T \F$
\end{definition}