3. 10 marks] Consider each of the following statements, assuming that all functions are non- negative: a) if fi (n) E (g(n)) and fa(n) E (g(n)), then fl (n)- (n) E 0(1); b) iffi (n) E 0(g(n)) and fa(n) E 0(m(n)), then fi (n)h(n) E (gi (n)g2(n)); c) if fi (n) E (g(n)) and fa(n) E (g(n)), then fl (n)(n) E (1); d) if log(f(n)) E O(log(g(n))) then f(n) E 0(g(n)). For each statement: if the statement is true then provide a proof that starts with the formal definition of the order notation utilized in the statement. If the statement is false provide a counter example and demonstrate why the statement is false