P 3.3.8 (12 pts) Problem: A chess knight, on one turn, moves either two squares vertically and one horizontally, or two horizontally and one vertically. If we consider a knight starting at the point (x, y) in Zx Z, it has eight possible moves, to (a +1, 4+2), (x +1, y 2), (x 1, y + 2), (w 1, y 2), (x + 2, y + 1), (x + 2, y 1), (x 2,y+1), or(x 2, y 1). (a) Prove that given any two points (x, y) and (a', y') in Z* Z, there is a sequence of knight moves from the first point to the second. (b) Let a and b be different positive naturals. An (a,b)-knight also has eight possible moves, from (x, y) to (x + a, y b) or (x + b, y a). What conditions on a and b allow the (a,b)-knight to go from any point in Zx Z to any other? Prove your answer. (c) If a and b do not meet the conditions of part (b), exactly which points can the (a,b)- knight reach from (x, y)