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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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What is the number of proper subsets of a given finite set with n element?
2n - 1
How many subsets are there in a set?
The number of subsets of a given set, including the set itself and the empty set, is 2n. Easiest way to see why: to make a particular subset, for each element in the original set you either chhose it or you don't. There are thus two possibilities for each element, so 2n possibilities for all n elements.
How many subsets does a set of n elements have?
2n. SeeHow_many_subsets_are_there_in_12_elements
What is the Formula for the number of subsets in a set?
If the set has n elements, the number of subsets (the power set) has 2n members.
How do you determine the number of subsets in relation to the universal set?
If the universal set, U, has N elements then it has 2N subsets.
