Prove whether each of the following statements are true or not. For those that you believe are false,

prove this by giving a counterexample (i.e. particular functions for f(n) and g(n) for which the given

statement is not true). For those that you believe are true, use the formal definitions of big-oh, big-Omega,

and big-Theta to prove it. In all problems, you are given that for all n, f(n) >= 0 and g(n) >= 0. 15

(a) Time complexity of T(n) = T(3n/4) + T(n/4) +n can be written as Omega(nlogn)

(b) f(n)+g(n) = O(max(f(n),g(n)))

(c) If f(n) = Omega(g(n)) then g(n) = O(f(n))