write a Prolog Program which describes a directed graph (G) (shown below)

A) write all possible node and edge facts that describes the structure of this graph G such as below:

node( a ). % a is a node of this graph.

edge( a, b ). % There is an edge (directed) from node a to b.

B) complete the definition all these rules.

node(X) :- % X is a node in graph G

edge( X, Y) :- % There is an directed edge from X to Y.

parent( X, Y) :- % There is a directed edge from X to Y.

child(X, Y) :- % Y is parent of X.

path( X, Y) :- % find a directed path from node X to node Y.

length_of_path( X, Y):- % Length of a path (directed) from X to Y.

connected( X, Y):- % There is a directed path from X to Y, or from Y to X

undirected_edge( X, Y) :- /* There is an edge (ignoring the directions) from X to Y or from Y to X */

undirected_path( X, Y) :- /* find a path (ignoring the directions) from node X to node Y. */

e a C e a C