Difference between subset and power set
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A set S is a subset of another set T if and only if every element in S can be found in T. ... The definition of subset relationship implies that for any set S, we always have ∅⊆S and S⊆S. The power set of a set S, denoted ℘(S), contains all the subsets of S. If |S|=n, then |℘(S)|=2n.
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