\begin{definition}[Definition:Event/Occurrence/Difference]
Let the probability space of an experiment $\EE$ be $\struct {\Omega, \Sigma, \Pr}$.
Let $A, B \in \Sigma$ be events, so that $A \subseteq \Omega$ and $B \subseteq \Omega$.
Let the outcome of the experiment be $\omega \in \Omega$.
Let $\omega \in A \setminus B$, where $A \setminus B$ denotes the difference of $A$ and $B$.
Then '''$A$ occurs but $B$ does not occur'''.
\end{definition}