Problem 2) (4.5 points): A relation R on the set of integers is given as follows: R = {(x, y) such that $x \le 3y + 4$}. Answer the following questions, and explain your answers. (a) Is R reflexive? (b) Is R symmetric? (c) Is R antisymmetric? (d) Is R transitive? (e) Is R an equivalence relation?
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In this case, we need to check if for every integer I, the statement 3I + 4 is true. If we substitute I with 0, we get 3(0) + 4 = 4, which is true. Show more…
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A relation R on the set of positive integers is given as follows: R = {(x, y) such that x ≥ 3y}. Answer the following questions, and explain your answers. (a) Is R reflexive? (b) Is R symmetric? (c) Is R transitive? (d) Is R an equivalence relation?
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