# Intersection

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In set theory, the intersection of two sets is the set of elements that they have in common: where denotes logical and. Two sets are disjoint if their intersection is the empty set.

## Properties

The intersection operation is:

• associative : ;
• commutative : .

## General intersections

### Finite intersections

The intersection of any finite number of sets may be defined inductively, as ### Infinite intersections

The intersection of a general family of sets Xλ as λ ranges over a general index set Λ may be written in similar notation as We may drop the indexing notation and define the intersection of a set to be the set of elements contained in all the elements of that set: In this notation the intersection of two sets A and B may be expressed as The correct definition of the intersection of the empty set needs careful consideration.