The drawing below shows a Hasse diagram for a partial order on the set {A, B, C, D, E, F, G, H, I, J} H E F 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 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 downward to the right of verter E. The edges, represented by line segments, between the vertices are as follows: Verter 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)
The drawing below shows a Hasse diagram for a partial order on the set {A, B, C, D, E, F, G, H, I, J} H E F 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 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 downward to the right of verter E. The edges, represented by line segments, between the vertices are as follows: Verter 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)
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 5SE: Answer the following questions. 5. What is the term for the arrangement that selects r objects from...
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Only Part 3 a and b please.
Transcribed Image Text:The drawing below shows a Hasse diagram for a partial order on the set {A, B, C, D, E, F, G, H, I, J}
H
E
F
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 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 downward to the right of verter E. The edges, represented
by line segments, between the vertices are as follows: Verter 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)
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