# Definition:Biconditional/Truth Table

## Definition

The characteristic truth table of the biconditional operator $p \iff q$ is as follows:

$\begin{array}{|cc||c|} \hline p & q & p \iff q \\ \hline \F & \F & \T \\ \F & \T & \F \\ \T & \F & \F \\ \T & \T & \T \\ \hline \end{array}$

### Matrix Form

$\begin{array}{c|cc} \iff & \T & \F \\ \hline \T & \T & \F \\ \F & \F & \T \\ \end{array}$

### Truth Table Number

The truth table number of the biconditional operator $p \iff q$ is as follows:

Ascending and descending order:

$1001$ or $\T \F \F \T$