Q-4: a) [5 marks) Let R be the partial order relation defined on A = {1, 2, 3, 4, 6, 8, 12}, where xRy means xy. Draw the Hasse diagram for R. b) [5 marks] Let g: R R, g(x) = 2x + 1. Show that g is both injective and surjective. c) (5 marks) Find the base-8 representation of 100 and base-9 representation of 1000. Show details of your work. d) [5 marks] Find all m > 1 such that 27 = 9 (mod m)