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I presume you meant 2^n (2 raised to the nth power), not 2*n (2 times n). That's answers.com's character set problem again (I trust, giving you the benefit of the doubt).

The answer is that for each of the n elements, it is either in any particular subset or it isn't. Which elements are in and which are not in a subset defines the subset. So for example, if n is 3, say a, b, and c, there are 2 sub-collections of the set of all subsets: those containing a and those not containing a. In each of those sub-collections, there are 2 sub-collections based on whether they contain b, for a total of 4 (2*2) sub-collections. Finally, of each of these 4, there are 2 subsets: those containing c and those not containing c, for a total of 8 (2*2*2 or 2^3) subsets. Got it?

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12y ago

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Q: Why does a set containing n element have 2n subsets?
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