(6) One way to prove a conditional statement is true, is to prove the contrapositive statement is true. Prove the following statement is true, by proving its contrapositive is true. "If x + y # Q, then x # Qor y # Q." (7) Recall that we define addition, subtraction, multiplication and division of rational numbers by: ad + bc a C ac d bd b d bd a C ad + bc ad bd bc (provided c # 0) Use these definitions to determine if the following statements are true or false. For each statement, if it's true, give a proof. If it's false, give an example showing why it's false. You may use without proof the fact that v2 # Q (since this was discussed in a tutorial problem). (a) If p, q E Q, then p + 2q E Q. (b) If p, q # Q and p # tq, then pq # Q. (c) If p, q E Q, then P-+9 E Q for all q E Q \\ {0}. (d) If p E Q and 2q # Q, then pq # Q. (8) In each case give an example of sets S, T C R satisfying the given conditions. (Be sure to demonstrate that your sets do, in fact, sastify the conditions.) (a) S and T are both infinite, but SOT has exactly 8 elements. (b) S is a closed interval, so that SnZ # SON. (c) S, T are open intervals (with S # T), and SUT = (a, b) where a