(17) Consider the following properties of binary relations: being reflexive, irreflexive, symmetric, asymmetric, antisymmetric, transitive, negatively transitive, serial, euclidean, and the compound properties of being an equivalence relation, partial order (reflexive, antisymmetric and transitive), or a preference relation (asymmetric and negatively transitive). For each of the binary relations defined below specify which of the properties listed above the given relation must satisfy. Present you results in a table. (a) Relation | on Z defined by: (x.y)elx divides y. (b) Relation, on Z defined by: x-, y5 divides (x-y). (c) Let G = (V,E) be a directed graph. Define a relation ( on V by: (x,y) e M, ? there is a directed path (in G) from x to y. (x,yje ?G-there is a directed path from x to y and from y to x A c B-A is a proper subset of B. (d) Let G = (V,E) be a directed graph. Define a relation ? on V by: (e) Let Sbe a set and P(S) the power set of S. Define a relation C on P(S), by