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? 0 (b) Is R2 reflexive? Justify your answer. Yes because when m = any integer ✓ then (m, m) E (c) Is R₂ symmetric? Justify your answer. Yes because 1, 2 V (1, R2 and ? ✓ 1 ? ✓ R2. (d) Is R2 transitive? Justify your answer. No because (0, 3 ✓ EV R2 and (1,?) ? R2, and ' ?v 2 ? R2. © } (N) Co
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? 0 (b) Is R2 reflexive? Justify your answer. Yes because when m = any integer ✓ then (m, m) E (c) Is R₂ symmetric? Justify your answer. Yes because 1, 2 V (1, R2 and ? ✓ 1 ? ✓ R2. (d) Is R2 transitive? Justify your answer. No because (0, 3 ✓ EV R2 and (1,?) ? R2, and ' ?v 2 ? R2. © } (N) Co
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?
0
(b) Is R2 reflexive? Justify your answer.
Yes
because when m = any integer ✓
then (m, m) E
(c) Is R₂ symmetric? Justify your answer.
Yes
because 1, 2 V
(1,
R2 and
? ✓
1 ? ✓ R2.
(d) Is R2 transitive? Justify your answer.
No
because (0, 3 ✓
EV R2 and
(1,?) ? R2, and
'
?v 2 ? R2.
© }
(N)
Co
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