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Unformatted text preview: n = 0 is also f ne; the only set with 0 elements is X = , which has exactly one subset, itself). If X has just one element, then there are two subsets: and X . For the inductive step, assume that X has n + 1 elements, of which one is colored red, the other n being blue. There are two types of subsets S : those that are solid blue; those that contain the red. By induction, there are 2 n solid blue subsets; denote them by B . But, there are as many subsets R containing the red as there are solid blue subsets: each R arises by adjoining the red element to a solid blue subset, namely, B = R { red } (even the singleton subset consisting of the red element alone arises in this way, by adjoining the red element to ). Hence, there are 2 n + 2 n = 2 n + 1 subsets....
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 Fall '11
 KeithCornell

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