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The set of all possible subsets of a set S is called the power set of S, written as P(S).
Examples ⇒
The power set of { ‘a’ } is { ∅, {‘a’} }
The power set of { 2, 3 } is { ∅, {2}, {3}, {2,3} }
The power set of {1, 2, 3 } is { ∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} }
If there are n members in a set S i.e. cardinality of set |S| = n, then there are 2n subsets possible.
Hence the power set would contain 2n elements. Or we can say that the cardinality of the power set is |P| is 2n.
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