Unformatted text preview: n as an element. Let B n denote the set of elements of K n that do not contain n as an element. Notice that A n and B n are disjoint sets and that K n = A n ∪ B n . 4(a). Write down the sets A 3 and B 3 . 4(b). Assume n > 2. Write down a rule that gives a bijection between A n and K n-2 . (You do not need to prove it is a bijection, just specify the rule.) 4(c). Assume n > 2. Write down a rule that gives a bijection between B n and K n-1 . (Hint: don’t try too hard.) 5. For n = 1 , 2 ,... , let k n = #( K n ). 5(a). Prove that if n > 2, k n = k n-1 + k n-2 . 5(b). How many subsets of the set A in Exercise 1 contain no consecutive pair of numbers? [You may assume the result of 5(a) if you did not prove it.]...
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- Fall '07
- Sets, #, Basic concepts in set theory, consecutive pair