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| Math Central | Quandaries & Queries |
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Question from Snehal, a student: 1. Let an denote the number of subsets of f{1,2, 3.... n}including the empty set and the set itself.) |
Snehal,
1. Each time you add a member to the set (in other words each time n increases by one), all the previous subsets still exist which do not include the number n, but now you can add the element n to each of them. This doubles the number of possible sets.
2. Hint: Think in binary: each member may be either in the subset or not in the subset. How many members are there? For help with the induction part of the question, take a look at our other induction questions in our archive for examples.
Cheers,
Stephen La Rocque.
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