Problem 3 Given a set A C R, we define the function fA : R - R by: fA(20) = 1 if x E A O if x & A a) Draw the graph of fo,1 and the graph of f[-1,1]U[2,3]. b) Show that fAnB = fA . fB c) Show that fAc = 1 - fA d) Show that if An B = 0 then fAUB = fA + fB. e) Is is true that in general fAUB = fA + fB