section_path: Basic operations
section_name: Basic operations
paragraph_text: Basic operations
  
  Suppose that a universal set U (a set containing all elements being discussed) has been fixed, and that A is a subset of U.
  
  Given any two sets A and B,
  
  Examples:
  
  The operations above satisfy many identities. For example, one of De Morgan's laws states that (A ∪ B)′ = A ′ ∩ B ′ (that is, the elements outside the union of A and B are the elements that are outside A and outside B).
  
  The cardinality of A × B is the product of the cardinalities of A and B.(This is an elementary fact when A and B are finite. When one or both are infinite, multiplication of cardinal numbers is defined to make this true.)
  
  The power set of any set becomes a Boolean ring with symmetric difference as the addition of the ring and intersection as the multiplication of the ring.