(b) Give an example of a binary tree T and nodes x and y in T such that x and y have the same level but different heights.
(c) First prove the proposition for the special case of complete binary trees. Explicitly state your proof strategy.
(d) Does the proposition remain true if the noun "height" is replaced by the noun "depth" or "level"? Prove your answers.
(e) Prove the proposition for the general case, in which the heap might not be a complete tree.
(f) Does your argument given in part (e) still hold if the noun "height" is replaced by the noun "depth"? If not, explicitly identify the first sentence of your proof that fails with this textual substitution. Is your answer to part (f) consistent with your answer to part (d)?