Relations (6 points) Let X a, b and Y (1,2) (a) Give the sets X Y and P(X Y). (b) How many possible relations exist from X to Y? (c) what does P(X Y) represent with respect to relations? (d) How many binary relations exist on the set C = {1, 2, 3, 4)? You do not need to list all such relations (10 points) For each part, describe a relation using the different representations asked for (a) Let A= {1,2, 3, 4, 5,6) (i) Write out the relation R on A that expresses divides), that is if z l y then (z, ye R, that is describe the relation using the set enumeration methods (list all elements of the set ii) Draw the relation as a digraph. (ii) Describe the relation as a zero-one matrix (assume rows/columns are ordered numeri- cally)