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Q6 [5 marks] Recall that the height of a binary tree is the longest path from the root node to any leaf node in the tree. For example, the height of the tree in Fig. 5 is 2 and the height of the tree in Fig. 6 is 4. Let T be the set of all binary trees that meet the following condition: for each non-leaf node in the tree, the heights of the left and right child differ by at most 1 . Provide a proof that for any tree in T, the number of nodes in the tree is at least 1.5 times the height of the tree, i.e., for any tree t in T, nodes (t)31.5 height (t)