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# What are the basic set operations?

There are several basic set operations, the most common being the intersection of sets, union of sets, and the complement of sets. The following lists these operations (note: the first two operations obey the associative and communtative laws, and together they obey the distributive law):

Intersection—The intersection of two sets is the set of elements common to the two sets. For example, the intersection of sets A and B is the set of elements common to both A ∩ B. This is usually written as A D B. Thus, if A = {1, 2, 3, 4} and B = {3, 4, 5}, then the intersection of A and B would be {3, 4}.

Union—The union of sets is the combining of members of the sets. For example, the union of two sets A and B is the set obtained by combining members of sets A and B. This is usually written as A ∪ B. Thus, if A = {1, 2, 3, 4} and B = {3, 4, 5}, then the union of A and B would be {1, 2, 3, 4, 5}.

Complement or complementation—When the set of all elements under consideration must be specified, it is called the universal set. And if the universal set is U = {1, 2, 3, 4, 5} and A = {1, 2, 3}, then the complement of A (or A’) is the set of all elements in the universal set that are not A, or {4, 5}. The intersection between a set and its complement is the empty or null set (∅); the union of a set and its complement is the universal set.

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