Definition:Class Difference

Definition

Let $A$ and $B$ be two classes.

The (class) difference $A \setminus B$ of $A$ and $B$ is defined as the class of all sets $x$ such that $x \in A$ and $x \notin B$:

$x \in A \setminus B \iff x \in A \land x \notin B$

or:

$A \setminus B = \set {x: x \in A \land x \notin B}$

Also see

• Definition:Set Difference, the usual presentation of this concept in set theory

• Results about class difference can be found here.

Sources

• 2002: Thomas Jech: Set Theory (3rd ed.) ... (previous) ... (next): Chapter $1$: Classes
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 5$ The union axiom: Boolean operations $(3)$