Problem 1 [24 pts (8,8,8): Growth of Functions i. Either prove true or give a counterexample of the following statement: If two functions f,g ii. Either prove true or give a counterexample of the following statement:If two functions f.g iii. Prove that (log2(n))3-0(n). Hints : satisfy f(n)/g(n) = (1) then they have same order of growth, ie, f = (g). have the same order of growth, ie, f = (g), then f(n)/g(n) = (1) First: Write the corresponding "big O" inequality-to-prove with chosen constant c4 Second: Since we care about asymptotic behavior for large n, we can change the variable n into 2"; write the new inequality. Third: Prove this inequality by induction over m, starting at mstart 4