R-2.8 Let T be a binary tree with n nodes, and let p be the level numbering of the nodes of T, so that the root, r, is numbered as p(r)1, and a node v has left child numbered 2p(v) and right child numbered 2p(v) 1, if they exist a. Show that, for every node v of T, p()2(+1)/21 b. Show an example of a binary tree with at least five nodes that attains the above upper bound on the maximum value of p(v) for some node v