Definition:Logical NAND/Boolean Interpretation

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

Let $\uparrow$ denote the logical NAND operator.

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


 * $\map v {\mathbf A \uparrow \mathbf B} = \begin {cases}

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