Let A = {1, 2, 3, 4, 5, 6, 7}, and let B be the set of all subsets of A. Then B (which is called the power set of A) is a set whose elements are sets. In particular, note that ∅ and A are both elements of B (since ∅ ⊆ A and A ⊆ A). Create a decision algorithm to determine n(B). Hint. Consider an arbitrary B ∈ B. Imagine how you might “construct” this set B, noting that, for each x ∈ A, there are 2 alternatives: Either x ∈ B or x /∈ B. Now, think about how many (distinct) sets can be made using this procedure.

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