I need 17 and 20 answered

Show that S_1 = S_2 if and only if (S_1 intersection S_2 bar) union (S_1 bar intersection S_2) = 0 Show that S_1 union S_2 - (S_1 intersection S_2 bar) = S_2 Show the distributive law S_1 intersection (S_2 union S_3) = (S_1 intersection S_2) (S_1 intersection S_3) holds for sets. Show that S_1 times (S_2 union S_3) = (S_1 times S_2) union (S_1 times S_3). Give conditions on S_1 and S_2 necessary and sufficient to ensure that S_1 = (S_1 union S_2) - S_2. Use the equivalence defined in Example 1.4 to partition the set {2, 4, 5, 6, 9, 22, 24, 25, 31, 37} into equivalence classes. Show that if f (n) = O (g(n)) and g(n)-O (f(n)), then f (n) = Theta(g(n)). Show that 2^n = O(3^n), but 2^n notequaltoTheta(3^n). Show that the following order-of-magaitude results hold. (a) n^2 + 5 log n = O(n^2) (b) 3^n = O(n!) (c) n! = O(n^n). Show that (n^3 - 2n)/(n + 1) = Theta(n^2). Show that n^3/log(n + 1) = O(n^3) but not O(n^2). What is wrong with the following argument? X = O(n^4), y = O(n^2), therefore x/y = O(n^2). What is wrong with the following argument? x = Theta(n^4), y = Theta(n^2), therefore