Definition:Logical NOR/Boolean Interpretation

Let $\mathbf A$ and $\mathbf B$ be propositional formulas.
Let $\downarrow$ denote the logical NOR operator.
The truth value of $\mathbf A \downarrow \mathbf B$ under a boolean interpretation $v$ is given by:
$v \left({\mathbf A \downarrow \mathbf B}\right) = \begin{cases} T & : v \left({\mathbf A}\right) = v \left({\mathbf B}\right) = F\\ F & : \text{otherwise} \end{cases}$