What is the cardinality of the power set P(S) where S is a set of 15 elements?
I think the power set is a set of all the subsets of a given set or 2n. So would the cardinality of this set be 215 or 32,768?
Answer
Yes, the cardinality of the power set P(S) of a set S is given by 2n, and so in your case, by 215.
Note: There is a difference between a set, and its cardinality. The power set P(S) itself is the set of all subsets of S, whereas 2n is the number of these sets (which are the elements) in P(S).
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