The set difference between two sets $X$ and $Y$ is
\[X \setdif Y = \{x \in X : x \notin Y\}.\]
For any set $X$:
- \[X \setdif \empt = X.\]
- \[\empt \setdif X = \empt.\]
- \[X \setdif X = \empt.\]
Any two sets $X$ and $Y$ are disjoint if and only if
\[X \setdif Y = X.\]
For any two sets $X$ and $Y$, if $X \subseteq Y$, then
\[X \setdif Y = \empt.\]