Intersection
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The intersection of two or more sets is the set of elements which are common to all of them. Thus, the intersection of the sets and is the set . The intersection of two or more sets is denoted by the symbol , so the preceding example could be written .
For any sets , and . Thus if and only if .
In geometry, a line may be considered to be a set of points with a particular property (the property of being on that line). Then the intersection of two lines reduces to the set definition of intersection.