PROBLEM 7 art 1. The drawing below shows a Hasse diagram for a partial order on the set A, B, C, D, E, F, G, H, I, J} J. igure 3: A Hasse diagram shows 10 vertices and 8 edges. The vertices, rep- esented by dots, are as follows: vertez J; vertices H and I are aligned vertically to ne right of vertez J; vertices A, B, C, D, and E forms a closed loop, which is to ne right of vertices H and I; vertez G is inclined upward to the right of vertez E; nd vertez F is inclined downward to the right of vertez E. The edges, represented y line segments, between the vertices are as follows: Vertez J is connected to no erter; a vertical edge connects vertices H and I; a vertical edge connects vertices and C; and 6 inclined edges connect the following vertices, A and B, C and D, and E, A and E, E and G, and E and F. (a) What are the minimal elements of the partial order? (b) What are the maximal elements of the partial order? (c) Which of the following pairs are comparable? (A, D), (J, F), (B, E), (G, F), (D, B), (C, F), (H, I), (C, E)
PROBLEM 7 art 1. The drawing below shows a Hasse diagram for a partial order on the set A, B, C, D, E, F, G, H, I, J} J. igure 3: A Hasse diagram shows 10 vertices and 8 edges. The vertices, rep- esented by dots, are as follows: vertez J; vertices H and I are aligned vertically to ne right of vertez J; vertices A, B, C, D, and E forms a closed loop, which is to ne right of vertices H and I; vertez G is inclined upward to the right of vertez E; nd vertez F is inclined downward to the right of vertez E. The edges, represented y line segments, between the vertices are as follows: Vertez J is connected to no erter; a vertical edge connects vertices H and I; a vertical edge connects vertices and C; and 6 inclined edges connect the following vertices, A and B, C and D, and E, A and E, E and G, and E and F. (a) What are the minimal elements of the partial order? (b) What are the maximal elements of the partial order? (c) Which of the following pairs are comparable? (A, D), (J, F), (B, E), (G, F), (D, B), (C, F), (H, I), (C, E)
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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![PROBLEM 7
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}
Ce
Figure 3: A Hasse diagram shows 10 vertices and 8 edges. The vertices, rep-
resented by dots, are as follows: verter J; vertices H and I are aligmed vertically to
the right of vertez J; vertices A, B, C, D, and E forms a closed loop, which is to
the right of vertices H and I; vertez G is inclined upward to the right of vertez E;
and vertez F is inclined downward to the right of verter E. The edges, represented
by line segments, between the vertices are as follows: Vertez J is connected to no
verter; a vertical edge connects vertices H and I; a vertical edge connects vertices
B and C; and 6 inclined edges connect the following vertices, A and B, C and D,
D and E, A and E, E and G, and E and F.
(a) What are the minimal elements of the partial order?
(b) What are the maximal elements of the partial order?
(c) Which of the following pairs are comparable?
(A, D), (J, F), (B, E), (G, F), (D, B), (C, F), (H, I), (C, E)
Part 2. Each relation given below is a partial order. Draw the Hasse diagram for
the partial order.
(a) The domain is {3, 5, 6, 7, 10, 14, 20, 30, 60}. z < y if r evenly divides y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf8aa82a-31a1-4382-a30e-3ad6a3174f84%2F7538388d-f49d-4a2a-9c8d-d8a2279b03dd%2F7ngc9k_processed.png&w=3840&q=75)
Transcribed Image Text:PROBLEM 7
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}
Ce
Figure 3: A Hasse diagram shows 10 vertices and 8 edges. The vertices, rep-
resented by dots, are as follows: verter J; vertices H and I are aligmed vertically to
the right of vertez J; vertices A, B, C, D, and E forms a closed loop, which is to
the right of vertices H and I; vertez G is inclined upward to the right of vertez E;
and vertez F is inclined downward to the right of verter E. The edges, represented
by line segments, between the vertices are as follows: Vertez J is connected to no
verter; a vertical edge connects vertices H and I; a vertical edge connects vertices
B and C; and 6 inclined edges connect the following vertices, A and B, C and D,
D and E, A and E, E and G, and E and F.
(a) What are the minimal elements of the partial order?
(b) What are the maximal elements of the partial order?
(c) Which of the following pairs are comparable?
(A, D), (J, F), (B, E), (G, F), (D, B), (C, F), (H, I), (C, E)
Part 2. Each relation given below is a partial order. Draw the Hasse diagram for
the partial order.
(a) The domain is {3, 5, 6, 7, 10, 14, 20, 30, 60}. z < y if r evenly divides y.
![(b) The domain is {a, b, c, d, e, ƒ}. The relation is the set:
{(ь, е). (6, d), (с, а). (с, f), (а, f), (а, а). (ь, b), (с, с). (а, d), (e, e), (f. f)}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf8aa82a-31a1-4382-a30e-3ad6a3174f84%2F7538388d-f49d-4a2a-9c8d-d8a2279b03dd%2Fzii7px_processed.png&w=3840&q=75)
Transcribed Image Text:(b) The domain is {a, b, c, d, e, ƒ}. The relation is the set:
{(ь, е). (6, d), (с, а). (с, f), (а, f), (а, а). (ь, b), (с, с). (а, d), (e, e), (f. f)}
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