What is a Power Set? | Set Theory, Subsets, Cardinality

What is a power set? A power set of any set A is the set containing all subsets of the given set A. For example, if we have the set A = {1, 2, 3}. Then the power set of A, denoted P(A), is {{ }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} where { } is the empty set. We also know that any set with n elements has a total of 2^(n) subsets, so if we have set B with n elements, it has 2^(n) subsets. This means that the cardinality of the power set of B would be 2^(n) also, since the power set contains all subsets of B. Thus, |P(B)| = 2^(n). I hope you find this lesson helpful.

Every set is an element of its power set:    • Every Set is an Element of its Power ...  

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