# 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 truth value of $\mathbf A \iff \mathbf B$ under a boolean interpretation $v$ is given by:

$\map v {\mathbf A \iff \mathbf B} = \begin{cases} \T & : \map v {\mathbf A} = \map v {\mathbf B} \\ \F & : \text{otherwise} \end{cases}$