1. Let A and B be two sets with maxima a and b, respectively. Show that max{a,b} is the maximum element of A U B. 2. For arbitrary sets A, B, and 0, show that A U (30 C) = (A U B) n {A UC) by showing that an element of the left-hand set must be an element of the right-hand one and vice versa. 3. Let f : IR\" !r R be a convex function. Show that the function g(x) = f(x) + c is convex for any constant c E R