Difference between revisions of "Intersection"
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− | The '''intersection''' of two or more [[set]]s is the set of [[element]]s which are common to all of them. Thus, the intersection of the sets <math>\{1, 2, 3\}</math> and <math>\{1, 3, 5\}</math> is the set <math>\{1, 3\}</math>. | + | The '''intersection''' of two or more [[set]]s is the set of [[element]]s which are common to all of them. Thus, the intersection of the sets <math>\{1, 2, 3\}</math> and <math>\{1, 3, 5\}</math> is the set <math>\{1, 3\}</math>. The intersection of two or more sets is denoted by the symbol <math>\cap</math>, so the preceding example could be written <math>\{1, 2, 3\} \cap \{1, 3, 5\} = \{1, 3\}</math>. |
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+ | For any sets <math>A, B</math>, <math>A \cap B \subset A</math> and <math>A \cap B \subset B</math>. Thus <math>A \cap B = A</math> if and only if <math>A \subset B</math>. | ||
Revision as of 14:28, 23 October 2006
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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.