Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily true that f(n) = O (h (n)). You may assume that low degree (i.e., low-exponent) polynomials do not dominate higher degree polynomials, while higher degree polynomials dominate lower ones. For example, n^3 notequalto O (n^2), but n^2 = O (n^3). Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily true that f (n) = Ohm (h (n)). Use the properties of Big-Oh, Big-Omega, and Big-Theta discussed in class to prove that if f (n) = n lg n - 10n + 42 and g (n) = theta (squareroot f (n)), then g (n)^2 + 2 g (n) + 1 = theta (n lg n). You may assume that 1 = O (n lg n), lg (n) = Ohm (1), and g (n) = Ohm (1)