Part 1: The drawing below shows a Hasse diagram for a partial order on the set: {4, B, C, D, E, F, G, H. I, J} BO F Figure 1: A Hasse diagram shous 10 vertices and 8 edges. The vertices, represented by dots, follows: verter J is upward of verter H: verter H is upward of verter I; erter B is inclined upwa the left of verter A: eerter C is upward of verter B; vertez D is inclined upward to the right of C: vertez E is inclined upward to the left of verter F; vertez G is inclined upward to the right of v E. The edges, represented by hine segments between the vertices are as follows: 3 vertical edges con the following vertices: B and C, H and I, and H and J; 5 inclined edges connect the following vert A and B, C and D, D and E, E and F, and E and G. Determine the properties of the Hasse diagram based on the following questions: (a) What are the minimal elements of the partial order? (b) What are the maximal elements of the partial order? (e) Which of the following pairs are comparable? (A, D). (J. F), (B, E), (G, F), (D, B), (C, F), (H, I). (C. E)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
Section: Chapter Questions
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Discrete Mathematics I need help with this two part problem Part 1 Part 2
o.tex- TeXstudio
label
tiny
3 of 14
Part 1: The drawing below shows a Hasse diagram for a partial order on the set:
(4. B. C. D, E, F. G, H. 1, J}
CO
B
Figure 1: A Hasse diagram shous 10 vertices and 8 edges. The vertices, represented by dots, are as
follows: verter Jis upeard of verter H: verter H is upward of verter I; vertez B is inclined upward to
the left of verter A: certer C is upward of erter B; vertez D is inclined upward to the right of verter
C: vertez E is inclined upward to the left of verter F; vertez G is inclined upuward to the right of vertez
E. The edges, represented by hine segments betwcen the vertices are as follows: 3 vertical edges connect
the following vertices: B and C, H and 1, andH and J; 5 inclined edges conneet the following vertices:
A and B. C and D, D and E. E and F, and E and G.
Determine the properties of the Hasse diagram based on the following questions:
(a) What are the minimal ekements of the partial order?
(b) What are the maximal elements of the partial order?
(e) Which of the following pairs are comparable?
(4, D). (J. F), (B, E), (G, F), (D, B), (C, F), (H, I), (C. E)
Transcribed Image Text:o.tex- TeXstudio label tiny 3 of 14 Part 1: The drawing below shows a Hasse diagram for a partial order on the set: (4. B. C. D, E, F. G, H. 1, J} CO B Figure 1: A Hasse diagram shous 10 vertices and 8 edges. The vertices, represented by dots, are as follows: verter Jis upeard of verter H: verter H is upward of verter I; vertez B is inclined upward to the left of verter A: certer C is upward of erter B; vertez D is inclined upward to the right of verter C: vertez E is inclined upward to the left of verter F; vertez G is inclined upuward to the right of vertez E. The edges, represented by hine segments betwcen the vertices are as follows: 3 vertical edges connect the following vertices: B and C, H and 1, andH and J; 5 inclined edges conneet the following vertices: A and B. C and D, D and E. E and F, and E and G. Determine the properties of the Hasse diagram based on the following questions: (a) What are the minimal ekements of the partial order? (b) What are the maximal elements of the partial order? (e) Which of the following pairs are comparable? (4, D). (J. F), (B, E), (G, F), (D, B), (C, F), (H, I), (C. E)
scoopedgar:0
wo.tex - TeXstudio
rt
label
tiny
4 of 14
Part 2: Consider the partial order with domain (3, 5, 6, 7, 10, 14, 20, 30, 60, 70} and with z Sy if
r evenly divides y. Select the correct Hasse diagram for the partial order.
60
70
30
20
14
10
3
(a)
7
Figure 2: A Hasse diagram shous a set of elements 3; 5: 6; 7: 10: 14: 20; 30; 60, 70.
There are lines connecting 3 and 6, 6 and 30, s0 and 60, 5 and 10, 10 and 20, 20 and 60, 10
and 70, 7 and 14. 14 and 70.
6,
Transcribed Image Text:scoopedgar:0 wo.tex - TeXstudio rt label tiny 4 of 14 Part 2: Consider the partial order with domain (3, 5, 6, 7, 10, 14, 20, 30, 60, 70} and with z Sy if r evenly divides y. Select the correct Hasse diagram for the partial order. 60 70 30 20 14 10 3 (a) 7 Figure 2: A Hasse diagram shous a set of elements 3; 5: 6; 7: 10: 14: 20; 30; 60, 70. There are lines connecting 3 and 6, 6 and 30, s0 and 60, 5 and 10, 10 and 20, 20 and 60, 10 and 70, 7 and 14. 14 and 70. 6,
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