Consider the simple directed graph shown below, with no cycles. 1. (2 pts) Use a relation to represent the connectivity of the nodes in Prolog. 2. (4 pts) Use rules and recursion to define a predicate path (x,y), showing whether there is a path between node x and node y. Use the program to give the check that there is of a path from A to E. What about the path from B to C ? 3. (2 pts) What does the query path (a,X) return? What if the graph had cycles (say by adding an arc from d to a)? Explain