. Let a and b be integers such that o 18 2 ma. + T1!) for some integers m and n; o 24 = 1m. + lb for some integers k and I; and 0 3|a. and 3|b but 3 % gcd(a,, b). Find gcd(a,, b). Justify your answer. . Let a, b, c, and d be positive integers such that I c : ma + sat: for some integers m and n; I d : k0. + lb for some integers k and l; and 0 l : gcd(c, d) Prove that l = gcd(a., b). . For 11:,y E R, dene (r 2 y to mean that my % 0. (a) Prove or disprove that 2 is reexive. (b) Prove or disprove that 2 is symmetric. (c) Prove or disprove that 2 is transitive. . Let RJF and Z+ denote the postive real numbers and positive integers, respectively. For 3:, y E R+, dene :1: 2 y to mean that 3 E Z+. (a) Prove or disprove that 2 is reexive. (b) Prove or disprove that 2 is symmetric. (c) Prove or disprove that 2 is transitive. . For A, B in MAR) (the set of all n X 7:. matrices with real entries), dene A N B to mean that there exists an invertible matrix P such that B : P'lAP. Prove that N is an equivalence relation on MAR)