Using only the formal definition of Big O, Big Omega, and Big Theta, prove the following. You do not have to show any pre-proof analysis, but make sure that you justify every step in the proof. 12n+5n-1 a. (n) n-1 b. 5n2 3n+2 0(n) - Using the formal definition of Big O, prove the transitive property: c. If d(n) = 0 (f(n)) and f(n) = O(g(n) then d(n) = 0 (g(n)) Using the rules on slide 9 of the Week 4 Merge Sort slides, prove the following. Make sure you cite the rules you are using at each step: d. 2n + 4n logn O(n)