Prove rigorously each of the following statements using the definition of O, Ohm, and Theta. Be sure to give values of c and n_0 that will make the argument work. a.(n^4 n^2 + n + 10 belongsto Ohm(n^3) b. In n belongsto Theta(lg n) c. (sigma^n/2_i = 0 i/3) 2n + lg n belongsto O(n^2) Give the asymptotic (Theta) bound for T(n) governed by each of the following recurrences. Justify your answers! a. T(n) = 6T(n/3) + 17n + log n. b. T(n) = 4T(n/2) + n^2 n. c. T(n) = T(n 3) + 1/2: T(0) = T(1) = T(2) = 1