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Similar to the connection of statements to get new statements, there are operations to make new sets from old ones. The most important operations are the following.[1]

  1. Union
  2. Intersection
  3. Difference set

For these operations to make sense, the sets need to be subsets of a common basic set. This ensures that we are talking about the same elements. Quite often this basic set is not mentioned explicitly and has to be understood from the context. A special case of the difference set is the complement of a subset in a given base set , also denoted as

If two sets have an empty intersection, meaning , we also say that they are disjoint.

  1. It is easy to memorize the symbols: the for union looks like u. The intersection is written as . The corresponding logical operations or, and have the analog form and respectively.