Set Operation

A set operation is a formal operation on (one or more) sets.

• Context:
  • It can be associated to a Set System.
  • It can be defined in terms of the Set Member Relation.
  • It can be a part of a Set Algebra.
  • It can range from being a One-Set Operation to being an n-Set Operation (such as a binary set operation).
• Example(s):
  • Fundamental Set Operation, such as:
    • Union Set Operation (A∪B).
    • Intersection Set Operation (A∩B).
    • Set Difference Operation (A\B)
    • Complement Set Operation (A\\B, A^U)
  • Set Relations, such as the subset relation ⊂, ⊄, and ⊆.
  • Set Functions, such as the set cardinality function |A|.
  • Set Symmetric Difference.
  • …
• Counter-Example(s):
  • a String Operation.
  • a Multiset Operation.
• See: Mathematical Operation, Commutative Set Law, Associative Set Law, Distributive Set Law, Identity Set Law, Complement Set Law.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/set_(mathematics)#Basic_operations Retrieved:2015-2-1.
  • There are several fundamental operations for constructing new sets from given sets.

2013

• (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/algebra_of_sets Retrieved:2013-12-13.
  • The algebra of sets defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.

    Any set of sets closed under the set-theoretic operations forms a Boolean algebra with the join operator being union, the meet operator being intersection, and the complement operator being set complement.

• (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/set_(mathematics)#Basic_operations Retrieved:2013-12-13.
  • There are several fundamental operations for constructing new sets from given sets.

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