Power Set and Universal Set

#Power Set

   Let  A = { a , b } then, Subset of A are  𝜱 , { a } , { b } and { a , b } .

   If we consider these subsets as elements of a new set B then, B = { 𝜱 ,{ a },{ b },{ a , b } }

   B is set to be the Power Set of A.

   Notation : Power set of a set A is denoted by P(A), and it is the set of all subsets of the

                          given set.

#Universal Set

   The set containing all objects or elements and of which all other sets are subsets.

    

    In other words : In a particular problem a set U is set to be a universal set if all the sets in

    that problem are subsets of U.

    Universal set is generally denoted by U.

#Remarks

• . Universal set does not mean a set containing all objects of the universe.
• . A set which is a universal set for one problem may not be a universal set for another problem.