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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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