If a subset of a contains n elements, how many subsets of a? How many nonempty subsets of a? How many nonempty proper subsets of a?

A subset of a set can contain any element in the set, or even an empty set, so each element in the set can be selected or not. Each element has two choices X 2 is 2 ^ n
There are 2 ^ n-1 nonempty subsets
There are 2 ^ n-2 nonempty proper subsets (minus the empty set and the set itself)

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