Problem 4: Graphs and Relations Consider an arbitrary directed graph G=(V,E). [a] How is E related to the concept of Cartesian product? [b] Let A be a binary relation over VXX such that vAw means that vertex v is adjacent to vertex w. Discuss whether the relation A is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, or transitive. [c] Let C be a binary relation over VXV such that vCw means that that vertex v is connected to vertex w. Discuss whether the relation C is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, or transitive. [d] Assuming we know all pairs of the relation A, how can we determine all pairs of the relation C