Answer: The following definitions are used: A relation on
Chapter 8, Problem 45E(choose chapter or problem)
Problem 45EThe following definitions are used: A relation on a set A is defined to beirreflexive if, and only if, for all x ∈ A, xx;asymmetric if, and only if, for all x, y ∈ A, if x R y then y x;intransitive if, and only if, for all x, y, z ∈ A, if x R y and y R z then x z.For each of the relations in the referenced exercise, determine whether the relation is irreflexive, asymmetric, intransitive, or none of these.ExerciseA number of relations are defined on the set A = {0, 1, 2, 3}. For each relation:a. Draw the directed graph.b. Determine whether the relation is reflexive.c. Determine whether the relation is symmetric.d. Determine whether the relation is transitive.Give a counterexample in each case in which the relation does not satisfy one of the properties.Exercise 1R3 = {(2, 3),(3, 2)}
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