# 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:

## 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.