(i) Let f: A -> R be a function and B C A. Define g: B -> R as g(r) = f(x) for all r E B. Prove or disprove the following statement: The function f is uniformly continuous if and only if g is uniformly continuous. (ii) Suppose f: (a, b) -> R is continuous and f(r) = 0 for each rational number r E (a, b). Show that f(x) = 0 for all r E (a, b)