Determine whether each of the following statements is true or false, and justify your answer. (a) f and g are uniformly continuous on a set S, then f+g is uniformly continuous on S. (b) If f and g are uniformly continuous on a set S, then fg is uniformly continuous on S. (c) If f is uniformly continuous on S and g is uniformly continuous on f(S), then gof is uniformly continuous on S.