Definition:Conditional/Truth Table/Number

Definition
The truth table number of the conjunction operator $p \land q$ is as follows:

Ascending order:
 * $1101$ or $TTFT$

Descending order:
 * $1011$ or $TFTT$

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 $TFTT$

Descending order:
 * $1101$ or $TTFT$

$\neg \left({p \implies q}\right)$:

Ascending order:
 * $0010$ or $FFTF$

Descending order:
 * $0100$ or $FTFF$

$\neg \left({q \implies p}\right)$:

Ascending order:
 * $0100$ or $FTFF$

Descending order:
 * $0010$ or $FFTF$