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Set Builder Notation (more symbols)


Thomas J. Fournier


  1. If one set, shares some of the same elements of another set, the subset or superset symbols can be used to indicate this. Since, every element in set A, is also included in set B. Set A would be considered a subset (⊆) of Set B. It could also be written that Set B is a superset (⊇) of Set A.
  2. Example:

    A = {1, 2, 3} ⊆ B = {0, 1, 2, 3, 4} or
    B = {0, 1, 2, 3, 4} ⊇ A = {1, 2, 3}

  3. Other symbols that may be used, to indicate a subset or a superset, are ⊄ and ⊅. The following, indicates that Set A is not a superset of Set B and Set B is not a subset of Set A.
  4. Example:

    A = {1, 2, 3} ⊉ B = {0, 1, 2, 3, 4} or
    B = {0, 1, 2, 3, 4} ⊈ A = {1, 2, 3}

  5. If both sets share all of the same elements they are considered equal. That is, if A ⊆ B and B ⊆ A. Order of the element or duplication is not a factor that is considered in this determination.
  6. Example:

    A = {0, 1, 2, 3, 4} and B = {2, 1, 0, 4, 3, 4}, Set A = B