Problem 3 [4+4+4+4=16 marks] Prove or disprove each of the following statements. To prove a statement, you should provide a formal proof that is based on the definitions of the order notations. To disprove a statement, you can either provide a counter example and explain it or provide a formal proof. All functions are positive functions. a) f(n) & 0(g(n)) and f(n) & w(g(n)) = f(n) O(g(n)) b) f(n) O(g(n)) and h(n) O(g(n)) = f() O(1) c) f(n) O(g(n)) = 2f(n) E O(29(n)) d) min(f(n), g(n)) ( 10.0m)