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Problem 5) Let T be a binary tree with n nodes, and let f() be the level numbering function of the positions of T, as given in Section 8.3.2. a. Show that, for every position p of T, f(p) 2^n 2. b. Show an example of a binary tree with seven nodes that attains the above upper bound on f(p) for some position p. Problem 6) Let T be an ordered tree with more than one node. Is it possible that the preorder traversal of T visits the nodes in the same order as the postorder traversal of T? If so, give an example; otherwise, explain why this cannot occur..

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- 1. problem 5 Let T be a binary tree with n nodes, and let f() be the level numbering function of the positions of T, as given in Section 8.3.2. a. Show that, for every position p of T, f(p) 2^n 2. b. Show an example of a binary tree with seven nodes that attains the above upper bound on f(p) for some position p. Problem 6 Let T be an ordered tree with more than one node. Is it possible that the preorder traversal of T visits the nodes in the same order as the postorder traversal of T? If so, give an example; otherwise, explain why this cannot occur.