1. Let f: X Y be a function and suppose that AB Y. Show that f^(-1) (AB)= f^(-

1. Let f: X Y be a function and suppose that AB Y. Show that f^(-1) (AB)= f^(-1)(A)f^(-1)(B) 2. Show by induction |a1+a2+a3+..+an|<= |a1|+|a2|+|a3|+..+|an| from j=1 to n for any aj Reals 3.Prove that if SR contains one of its upper bound then this upper bound must be the sup of . Prove sup{2/n: n is a natural} =2 4. If S is not empty and has at least 2 components. Let S be bounded below and only [xy]S for any xy elements of S. Show S is an interval. Additional Requirements Level of Detail: Show all work Other Requirements: please show step by step