Definition:Set Difference

Definition
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:
 * $S \setminus T = \set {x \in S: x \notin T}$
 * $S \setminus T = \set {x: x \in S \land x \notin T}$

Also see

 * Definition:Set Union
 * Definition:Set Intersection
 * Definition:Symmetric Difference


 * Definition:Class Difference, the same concept in the context of class theory