Problem 1: [20 pts] (Sets and Functions) A major goal of this course is learning how to write careful proofs by utilizing definitions of the concepts we discuss. A good strategy is to do the following. . Write out relevant definitions for what you are asked to show. . Write out relevant definitions for what you are given. . Think about how what you're given relates to what you want to show. How can you can use the definitions of what you are given to show what you want to prove? . Make sure to introduce any quantities that you use in your solution that are not given in the statement of the problem. A. [10 pts] Let S= {(x,y) ER' |x 20,y 2 0). Show that S is a closed subset of IR-. B. [10 pts] Suppose that f : R -> R and g : R - R. Prove or disprove the following. i. If f and g are one-to-one, then fog is one-to-one. ii. If f and g are onto, then fog is onto