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Let A = {0, 1, 2, 3), and define a relation R, on A as follows: R₂ = (0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)}. (a) Which of the following is the directed graph of R₂? (b) Is R, reflexive? Justify your answer. ✓, because when m = 0 Yes (c) Is R, symmetric? Justify your answer. No (d) Is R₂ transitive? Justify your answer. Yes DO ✓, because (1, 0) EVR₂ and (1,1) EVR₂. ✓, because , then (m, m) E R₂. (0, 2) EVR₂ and (1, 1) EVR₂, and (1, 2) EVR₂. DO O

Let A = {0, 1, 2, 3), and define a relation R, on A as follows: R₂ = (0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)}. (a) Which of the following is the directed graph of R₂? (b) Is R, reflexive? Justify your answer. ✓, because when m = 0 Yes (c) Is R, symmetric? Justify your answer. No (d) Is R₂ transitive? Justify your answer. Yes DO ✓, because (1, 0) EVR₂ and (1,1) EVR₂. ✓, because , then (m, m) E R₂. (0, 2) EVR₂ and (1, 1) EVR₂, and (1, 2) EVR₂. DO O

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let A = {0, 1, 2, 3}, and define a relation R₂ on A as follows: R₂ = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2,3)}. (a) Which of the following is the directed graph of R₂? O (b) Is R, reflexive? Justify your answer. because when m = 0 Yes 2 (c) Is R₂ symmetric? Justify your answer. No Yes , (d) Is R₂ transitive? Justify your answer. (3 3 ✓, because (0, 2 i C because (1, 0) R₂ and (1, 1) EVR₂. then (m, m) E R₂. (0, 2) EVR₂ and (1, 1) EVR₂, and (1, 2) EVR₂. 3 Co Ce
Transcribed Image Text:Let A = {0, 1, 2, 3}, and define a relation R₂ on A as follows: R₂ = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2,3)}. (a) Which of the following is the directed graph of R₂? O (b) Is R, reflexive? Justify your answer. because when m = 0 Yes 2 (c) Is R₂ symmetric? Justify your answer. No Yes , (d) Is R₂ transitive? Justify your answer. (3 3 ✓, because (0, 2 i C because (1, 0) R₂ and (1, 1) EVR₂. then (m, m) E R₂. (0, 2) EVR₂ and (1, 1) EVR₂, and (1, 2) EVR₂. 3 Co Ce
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