[14 marks] Properties of Asymptotic Notation. Prove or disprove each of the following statements You may use the "max", ceiling, and floor functions in your solutions. However, you may not use any external facts of Big-Oh/Omega/Theta, and instead should only be using their definitions in your proofs The following definitions apply to part (d) Definition 1 (non-decreasing). Let f NR20. We say that f is non-decreasing if and only if for all a, y N. if x