4. (15 points) This question is about relations. (a) (13} Let R be the relation on the set Z dened as follows: ng; means \"a: g y + 1\". Is R reflexive? Symmetric? Transitive? Antisymmetric? For each of these properties, prove or disprove that it has that property. Is R an equivalence relation? Is R. a partial order? Let A = {0, 1}. There are 23 = 8 different ways of combining the properties reexive, symmetric and transitive in a relation. For example, a relation might have all three properties, or none of them, or some but not others. For each of these 8 possible combinations, construct a relation R on A that has these properties and draw its relation diagram, or motivate why such a relation cannot exist. Note that A only contains two elements