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)

Question
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)
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Transcribed Image Text

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)

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