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[15 13135] A binary tree is fail if every nonleaf node has exactly two children. For context1 recall that we saw in lecture that a binary tree of height h can have at most 2h+1 1 nodes, and that it achieves this maximum if it is complete, meaning that it is full and all leaves are at the same distance from the root. Find uUi), the minimum number of nodes that a full tree of height h can haveJ and prove your answer using ordinary induction on 11. Note that tree of height of 0 is a single (leaf) node Hint 1: try a few simpie cases (h = 0, 11 2,3, . . .) and see if you can guess what ,uUi) is