2- Prove thatthe following statements are true (7) or false (F). (let log n = log2n). You must define first what you are trying to prove using the limit definition. a) n³/logn O(n), for any integer constant 2 ≤ k≤ 4. b) n+nlogne (n²), for any positive integer constant k. c) nlogn³ O(n), for any integer constant k>2.

= For integer n ≥ 1 let P(n) be the predicate that 9" - 5n CEZ 4c for some For the induction hypothesis, consider k ≥ 1, and suppose that P(k) is true. For the inductive step, we want to show that P(k+1) is true. True or false: The following proof correctly proves P(k+ 1) true, where every step other than the one labelled IH follows by algebra. (I'm asking: is this a valid algebraic proof? Is the algebra correct? Did I use the IH correctly? Did I get the correct final result?) 9k+15k+19.9k - 5.5k True False = 9(4c – 5k) – 5 ⋅ 5% for CE Z by the IH = 4.9c-9.5k - 5.5k = 4.9c-4.5k = 4d for d = Z

make mathlab code

What do I do for (K + 1)? Please explain as best as possible