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Power set
The set of all the subsets of a set S is called the power set of S and denoted by  . Thus
Note the following
- A collection of sets is called a class of sets. Each element of a class is a set. Thus is a class.
- If S contains n elements, contains
 elements.
- If S is finite, then is closed under the set theoretic operation of unions, intersection and complementation,
Thus for all  ,
- If S is an infinite set, may not be closed under countably infinite unions or countably infinite intersections. Such situations lead to serious mathematical problems.
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