Exercise 5

Math Dec 23, 2022

Exercise 5.43. Consider the relation ~on N defined by r ~ y iff there exists & E Z such that r = 2*y. For each the following, unravel the definition of ~ to write out a sentence in a form similar to "If then " for what needs to be proven: (a) ~ is reflexive, (b) ~ is symmetric, (c) ~ is transitive, and (d) if x ~y, then ry or yr. Statement 5.44. Let ~ denote the relation from Exercise 5.43. Then ~ is an equivalence relation.