1. (30 pts) Let A = {4, 5, 6} and B = {5,6, 7} and define relations R, S, and T from A to B as follows: For all (x,y)e AXB, (x,y)e R means that x 2y , x_yeZ, 2 T = {(4,7),(555),(6,7)}. 3) Draw arrow diagrams for each of the relations. You should have 3 separate diagrams. (x,y) E 5 means that h) Are any of these relations also functions? For each relation, explain clearly in words why or why not. 2. (40 pts) Let X = {1,2,3}, Y = {4,5,6}, Z= {7,8,9} and let f : X-> Y and g :Y -> Z be functions defined by f = {(1,5),(2,5),(3,6)} and g = {(4,9),(5,7),(6,8)}. a. Draw arrow diagrams for fand g. You should have 2 separate diagrams. b. What is the domain of f? c. What is the co-domain of f ? d. What is the range of f? e. Let A = {2,3} . What is f (A)? f. Let B = {5}. What is f-(B)?3. (30 pts) If f : X - Y and g :Y - Z are functions and go f is one-to-one, is gone-to-one? Prove or give a counterexample