Definition:Biconditional/Boolean Interpretation

Definition
Let $\mathbf A$ and $\mathbf B$ be propositional formulas.

Let $\mathbf A \iff \mathbf B$ denote the biconditional operator.

The boolean interpretations for $\mathbf A \iff \mathbf B$ under the model $\mathcal M$ are:


 * $\left({\mathbf A \iff \mathbf B}\right)_\mathcal M = \begin{cases}

T & : \mathbf A_\mathcal M = \mathbf B_\mathcal M \\ F & : \text {otherwise} \end{cases}$