Definition:Exclusive Or/Boolean Interpretation

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

Let $\oplus$ denote the exclusive or operator.

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


 * $v \left({\mathbf A \oplus \mathbf B}\right) = \begin{cases}

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