Biconditional is Commutative/Formulation 1/Proof by Truth Table

Theorems

 * $p \iff q \dashv \vdash q \iff p$

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connectives match for all boolean interpretations.

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