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), (D, B), (С, F), (П, І), (С, E)

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), (D, B), (С, F), (П, І), (С, 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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Question

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), (D, B), (С, F), (П, І), (С, E)

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