3' Let S (_I R. SUPPOSG {fa} and {9n} are sequences of functions such that fn > f uniformly on S and 9,; > g uniformly on S, (a) Suppose fn is bounded on S for each n E N. Then Show that {fn} is uniformly bounded on S, which means that there exists M E R such that |fn(m)| S M for all a\" e S and for all n 6 N. (b) Prove that f5.1 + g\" > f + g uniformly on S. (c) Prove that if fn and g\" are bounded on S for each n E N, then fngn > f g uniformly on S