Part 1: The drawing below shows a Hasse diagram for a partial order on the set: (4, В, С, D, E, F, G, H, І, J G E H B F Figure 1: A Hasse diagram shows 10 vertices and 8 cdges. The vertices, represented by dots, are as follows: verter J is upward of verter H; verter H is upward of verter I; verter B is inclined upward to the left of verter A; verter C is upward of verter B; verte D is inclined upward to the right of verter C; verter E is inclined upward to the left of verter F; verter G is inclined upward to the right of verter 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? (b) What are the maximal elements of the partial order? (c) Which of the following pairs are comparable? (А, D), (J, F), (в, Е), (G, F), (D, в), (С, F), (Н, Г), (С, E)

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Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.