Part 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} D E IN B H Figure 1: A Hasse diagram shows 10 vertices and 8 edges. The vertices, represented by dots, are as follows: vertex J is upward of vertex H; verter H is upward of vertex I; vertex B is inclined upward to the left of vertex A; verter C is upward of vertex B; vertex D is inclined upward to the right of vertex C; vertex E is inclined upward to the left of vertex F; vertex G is inclined upward to the right of vertex E. The edges, represented by line segments between the vertices are as follows: 3 vertical edges connect the following vertices: B and C, H and I, and H and J; 5 inclined edges connect the following vertices: A and B, C and D, D and E, E and F, and E and G. F Determine the properties of the Hasse diagram based on the following questions: (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 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} D E IN B H Figure 1: A Hasse diagram shows 10 vertices and 8 edges. The vertices, represented by dots, are as follows: vertex J is upward of vertex H; verter H is upward of vertex I; vertex B is inclined upward to the left of vertex A; verter C is upward of vertex B; vertex D is inclined upward to the right of vertex C; vertex E is inclined upward to the left of vertex F; vertex G is inclined upward to the right of vertex E. The edges, represented by line segments between the vertices are as follows: 3 vertical edges connect the following vertices: B and C, H and I, and H and J; 5 inclined edges connect the following vertices: A and B, C and D, D and E, E and F, and E and G. F Determine the properties of the Hasse diagram based on the following questions: (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)
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 18E: Broadway The ordered pairs below give the starting year and gross ticket sales S (in millions of...
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Transcribed Image Text:### Part 1: Hasse Diagram Analysis
The drawing below shows a Hasse diagram for a partial order on the set:
$$ \{A, B, C, D, E, F, G, H, I, J\} $$
**Figure 1**: A Hasse diagram shows 10 vertices and 8 edges. The vertices, represented by dots, are as follows:
- Vertex \( J \) is upward of vertex \( H \)
- Vertex \( H \) is upward of vertex \( I \)
- Vertex \( B \) is inclined upward to the left of vertex \( A \)
- Vertex \( C \) is upward of vertex \( B \)
- Vertex \( D \) is inclined upward to the right of vertex \( C \)
- Vertex \( E \) is inclined upward to the left of vertex \( F \)
- Vertex \( G \) is inclined upward to the right of vertex \( E \)
The edges, represented by line segments between the vertices are as follows:
- 3 vertical edges connect the following vertices: \( B \) and \( C \), \( H \) and \( I \), and \( H \) and \( J \)
- 5 inclined edges connect the following vertices: \( A \) and \( B \), \( C \) and \( D \), \( D \) and \( E \), \( E \) and \( F\), and \( E \) and \( G \)
### Exercises:
Determine the properties of the Hasse diagram based on the following questions:
**(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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