What are the minimal elements of the partial order? What are the maximal elements of the partial order? Which of the following pairs are comparable? (A, D), (J. F). (B, E). (G, F). (D. B). (C, F). (H, I), (C. E)

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Chapter2: Second-order Linear Odes
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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, 1, J}
D
G
Figure 3: A Hasse diagram shous 10 vertices and 8 edges. The vertices, rep-
resented by dots, are as follows: vertez J; vertices H 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 H and I; verter G is inclined upward to the right of verter E;
and verter F is inclined dounward to the right of verter E. The edges, represented
by line segments, between the vertices are as follows: Verter J is connected to no
rerter; 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.
What are the minimal elements of the partial order?
What are the maximal elements of the partial order?
Which of the following pairs are comparable?
(4, D), (J, F), (В, Е). (G, F). (р, в), (С, F), (Н, 1). (С. Е)
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, 1, J} D G Figure 3: A Hasse diagram shous 10 vertices and 8 edges. The vertices, rep- resented by dots, are as follows: vertez J; vertices H 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 H and I; verter G is inclined upward to the right of verter E; and verter F is inclined dounward to the right of verter E. The edges, represented by line segments, between the vertices are as follows: Verter J is connected to no rerter; 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. What are the minimal elements of the partial order? What are the maximal elements of the partial order? Which of the following pairs are comparable? (4, D), (J, F), (В, Е). (G, F). (р, в), (С, F), (Н, 1). (С. Е)
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Step 1

 The minimal element is an element which is not greater than any other element

Therefor I, A ,F are minimal elements

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