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Operations on Sets

  1. Union of Sets If two sets are A and B, then union of A and B is defined as the set that have all the elements which belong to either A or B or both. It is represented by A  B.
  2. Intersection of Sets If two sets are A and B, then the intersection of A and B is defined as the set that have all the elements which belong to both A and B.
    It is represented by A  B.
     
    For example, find A ∪ B and A ∩ B if A = {1, 2, 3, 4, 5} and B = {2, 4, 6}
    A ∪ B = {1, 2, 3, 4, 5, 6}
    A  B = {2, 4}
     
    Description: 17-2.tif
  3. Disjoint Sets Two sets are said to be disjoint if A  B = 0, that is, not a single element is common to both of these two sets.
     
    For example, If A = {Set of all odd numbers} and B = {Set of all even numbers} then set A and set B are disjoint sets.
     
    Description: 17-3.tif
  4. Difference of Sets For two sets A and B, A – B is the set of all those elements of A that do not belong to B. Similarly, B – A is the set of all those elements of B that do not belong to A.
     
    For example, A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 8}, then A – B = {1, 3, 5, 6,} and B – A = {8}
     
    Description: 17-4.tif
  5. Complement of a Set If U is the universal set and a set A is such that A ⊆ U then complement of the set A is defined as U – A and represented as A’ or Ac
     
    For example, U = {Set of all prime numbers} and A = {Set of all even prime numbers} then U – A = {Set of all odd prime numbers}





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