snhu PROBLEM 2 This question has 2 parts. Part 1: The drawing below shows a Hesse diagram for a partial order on the set: {24,310,291 E, F, G, H, I, J} D G A 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 (7; 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. Determine the properties of the Hasse diagram based on the following questions: (a) What are the minimal elements of the partial order? ('0) What are the maximal elements of the partial order? ((3) Which of the following pairs are comparable? (A: D}: (J: F): (B: E): (G: F): (D: B): (C: F): (H: IMQ El snhu Part 2: Consider the partial order with domain {3, 5, 6, 7, 10, 14, 20, 30, 60, 70} and with x g y if x evenly divides y. Select the correct Hasse diagram for the partial order. 60 70 30 20 14 6 10 3 5 T (a) Figure 2: A Hesse diagram shows a set of elements 3; 5; 6; '7; 10; 14; 20; 30; 60, '70. There are tines oonnecttng 3 and 6, 6 and 30, 30 and 60, 5 and 10, 10 and 20, 20 and 60, 10 and 70, '7 and 14, 14 and 70. snhu 60 7O 30 20 14 6 10 3 5 7 (b) Figure 3: A Hesse diagram shows a set of elements 3; 5; 6; 7; 10; 14; 20; 30; 60, '70. There are lines connecting 3 and 6, 6 and 30, 36 and 60, 5 and 10, 10 and 30, 10 and 20, 20 and 60, 10 and 76, '7 and 14, 14 and '76. snhu 60 70 30 20 14 10 1 - 5 7 (c) Figure 4: A Hasse diagram shows a set of elements 3; 5; 6; 7; 10; 14; 20; 30; 60, 70. There are lines connecting 3 and 6, 6 and 30, 30 and 60, 5 and 10, 10 and 30, 10 and 20, 20 and 60, 20 and 70, 7 and 14, 14 and 70.snhu 30 20 14 6 10 | I 3 5 7 (d) Figure 5: A Hesse diagram shows a set of elements 3; 5; 6; 7; 10; 14; 20; 30; 60, '70. There are lines connecting 3 and 6, 6 and 30, 30 and 60, 5 and 10, 10 and 30, 10 and 20, 20 and 30, 20 and 60, 10 and '70, 7 and 14, 14 and '70