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 $\{1, 2, 3\}$ and $\{1, 3, 5\}$ is the set $\{1, 3\}$ . The intersection of two or more sets is denoted by the symbol $\cap$ , so the preceding example could be written $\{1, 2, 3\} \cap \{1, 3, 5\} = \{1, 3\}$ .

For any sets $A, B$ , $A \cap B \subset A$ and $A \cap B \subset B$ . Thus $A \cap B = A$ if and only if $A \subset B$ .

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. This also extends to other curves and surfaces.

Especially in the geometric context, two objects are said to intersect if their intersection is non- empty.

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Intersection

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