PROBLEM 7Part 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}CeFigure 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 tothe right of vertez J; vertices A, B, C, D, and E forms a closed loop, which is tothe 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, representedby line segments, between the vertices are as follows: Vertez J is connected to noverter; a vertical edge connects vertices H and I; a vertical edge connects verticesB 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 forthe 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)}

Answered: Image /qna-images/answer/7538388d-f49d-4a2a-9c8d-d8a2279b03dd.jpg

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.

(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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The drawing below shows a Hasse diagram for a partial order on the set {A, B, C, D, E, F, G, II, I, J} Figure 3: A Hasse diagram shous 10 vertices and 8 edges. The vertices, rep- resented by dots, are as follows: verter J; vertices II and I are aligned vertically to the right of verter J; vertices A, B, C, D, and E forms a closed loop, which is to the right of vertices II and I; vertex G is inclined upward to the right of vertex E; and vertex F is inclined downward to the right of vertex E. The edges, represented by line segments, between the vertices are as follows: Verter J is connected to no vertex; a vertical edge connects vertices II 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 B, Е аnd G, and E аnd P. (n) 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? (А, D), (J, F), (В, E), (G, F),…
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