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Intersection of Sets

In the set operations, let's calculate intersection of sets. The intersection of two sets A and B is the set that contains exactly all the elements that are in both A and B.

Intersection of Sets

For two given sets A and B, A∩B (read as A intersection B) is the set of common elements that belong to set A and B. The number of elements in A∩B is given by n(A∩B) = n(A)+n(B)−n(A∪B), where n(X) is the number of elements in set X. To understand this set operation of the intersection of sets better, let us consider an example: If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then the intersection of A and B is given by A ∩ B = {3, 4}.

Set Operations Table

Set OperationVenn DiagramInterpretation
UnionUnionA U B, is the set of all values that are a member of A, or B, or both.
IntersectionIntersectionA ∩ B, is the set of all values that are a member of both A and B.
DifferenceDifferenceA \ B, is the set of all values of A that are not members of B.
Symmetric DifferenceSymmetric DifferenceA ∆ B, is the set of all values which are in one of the sets but not both.
Intersection of Sets

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