1 . Let x e R. Prove that if (9x + 1)/999 is rational number, then x is also rational. Before the proof, you must specify the name of the method used clearly. (14 marks) 2. Use substitution method to prove that (Q A (P = R)) = (QvR) is a tautology. (14 marks) 3. Let x, y and z be simple statements. Determine whether the following compound statement is a tautology, contradiction or contingent statement: (VAX = ~zVy) = ~(YAz) (14 marks) 4. Suppose me Z. Ifm is odd, use direct proof prove that m - 2m - 9 is even. (14 marks) 5. Prove using mathematical induction that if a and r are real numbers and r # 1, Ear = a(ph+1 - 1) r- 1 1=0 for all n 2 0. (15 marks)