Simplify each of the following as much as possible. For example, ( )(3d : 2a) simplifies in ( )(e). (ll a. O(5) b. O(logs a) int: A few are already as simple as possible. ) Solution Answer for Question: Part A: O(5) it is already a simplified constant value . Part B: O(log3 A) it is already a simplified constant value . Part C: O(log a + 1) Here 1 is constant we can igore the constant 1. Resulting is O(log a) Part D: O(log a^2) => 2 O(log a) Refer ( logb(x y) = y logb(x)) Resulting is O(log a) where 2 is constant Part E: O((log a)^2) => Consider it has the Base b So b (log 2 a ) where 2 is the base. Part F : I don\'t the have symbol pi pi (a + log a) => we can devide the pi(a ) + pi (log a) Part g: pi(log a + 1) here 1 is constant . pi(log a) Part H: pi(max(a^2, a) => pi(a^2) will be the result. Part I: Pi(2^n + n^100) => Pi(n^100) will be the result. Part J: Theta(a^2 + 2a) => a Theta(a + 2) => Theta(a^2) Part K: Theta( 3n^2 + 2n + log n + 1) => n Theta(3n + 2 + logn + 1) Ignore constants .. => Theta(n^2 + logn ) Part I: Theta(n2^n) => no modifications Part M: Theta(3^n + 2^n) => not sure .