QUESTION 5 (4 points). A finite state machine M = {S,P,0,0, w} has P = 0 = {1,2,3} and is determined by the following state diagram: Start 32 3,3 3 (1) (1 point) Find the output for the input string = = 2123. (2) (2 points) Give the transition table for this machine. (3) (1 point) Determine all possibilities for x, such that w(s,, z) = 323311. QUESTION 6 (6 points). Let A = {1,2,3, 6, 5, 10, 12, 18). Define a relation R on A by XRy if and only if y divides z. (1) List, if any, the maximal element(s). (2) List, if any, the minimal element(s). (3) List, if any, the greatest element(e). (4) List, if any, the least element(e). (5) Let B = {2,3,6), find glb(B) (6) Let C = {2,3,6), find lub(C)