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.

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

$\blacksquare$