# Definition:Conjunction/Boolean Interpretation

## Definition

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

Let $\land$ denote the conjunction operator.

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

$v \left({\mathbf A \land \mathbf B}\right) = \begin{cases} T & : v \left({\mathbf A}\right) = v \left({\mathbf B}\right) = T \\ F & : \text{otherwise} \end{cases}$