MATH 1.1 : Introduction of Sets

• Set: a collection of well defined and distinct objects
• Roster Form - In this form, all elements of a set are listed and enclosed in braces. Elements are separated by a comma.
• Set-builder Form - In this form, a common property of all the elements of a set is written.
• Subset - A set A is said to be a subset of set B if all the elements of A are contained in B. That is c B

  _

  If the subset does not contain all the elements of a set, a proper subset notation c is used.

  ex: if A= {1,2,3,4,}

  B= {0,1,2,3,4,5,6,7}

  then A c B

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• Empty set or Null set - A set with no elements

  
  

  ex: A = {}
• Universal set ( denoted by U) - The set containing all objects or elements and of which all other sets are subsets.

  ex: A = {1,3,5,7}

  B = {2,4,6,8}

  U = {1,2,3,4,5,6,7,8}
• Cardinality of a Set - number of elements in a set. Denoted by set A as IAI .

  
  

  ex: A = {0,2,4,6,8}

  IAI = 5
• ●A set is a collection of well-defined and distinct objects.
• ●A set is in roster form if all elements of a set are listed and enclosed in braces. The elements are separated by a comma.
• ●A set is in set-builder form when a common property of all the elements of a set is written.
• ●Empty or Null Set is a set with no elements.
• ●Proper Subset is a subset which does not contain all the same elements of a set.
• ●A set is said to be a subset of another set if all the elements of it are contained in another set.
• Universal Set - containing all the elements of all related sets. Denoted by U
• Cardinality of a set - the number of elements in a set