# Definition:Class Intersection

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## Definition

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

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

$x \in A \cap B \iff x \in A \land x \in A$

or:

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

### Class of Sets

Let $A$ be a class.

The intersection of $A$ is:

$\ds \bigcap A := \set {x: \forall y \in A: x \in y}$

That is, the class of all objects which belong to all the elements of $A$.

## Also see

• Results about class intersections can be found here.

## Internationalization

Intersection is translated:

 In German: durchschnitt (literally: (act of) cutting) In Dutch: doorsnede