\begin{definition}[Definition:Set Difference]
The '''(set) difference''' between two sets $S$ and $T$ is written $S \setminus T$, and means the set that consists of the elements of $S$ which are not elements of $T$:
:$x \in S \setminus T \iff x \in S \land x \notin T$
It can also be defined as:
:$S \setminus T = \set {x \in S: x \notin T}$
:$S \setminus T = \set {x: x \in S \land x \notin T}$
\end{definition}