PROBLEM 7Part 1. The drawing below shows a Hasse diagram for a partial order on the set{4, B, C, D, E, F, G, H, 1, J}DGFigure 3: A Hasse diagram shous 10 vertices and 8 edges. The vertices, rep-resented by dots, are as follows: vertez J; vertices H and I are aligned vertically tothe right of verter J; vertices A, B, C, D, and E forms a closed loop, which is tothe right of vertices H and I; verter G is inclined upward to the right of verter E;and verter F is inclined dounward to the right of verter E. The edges, representedby line segments, between the vertices are as follows: Verter J is connected to norerter; a vertical edge connects vertices H and I; a vertical edge connects verticesB 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.What are the minimal elements of the partial order?What are the maximal elements of the partial order?Which of the following pairs are comparable?(4, D), (J, F), (В, Е). (G, F). (р, в), (С, F), (Н, 1). (С. Е)

Answered: What are the minimal elements of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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The domain of a relation A is the set of integers. x is related to y under relation A if x = y + 2. The relation B is the reflexive closure of the transitive closure of A.(a) Is A partial order? Is A total order? Justify both your answers. (b) Is B partial order? Is B total order? Justify both your answers.
Draw the Hasse diagram for the following partial order.
The figure below is a Hasse diagram for a partial order: F LL G O E, D, F, H O E, D H ΟΕ O E, D, H A E What are the minimal elements? B C D
Draw the Hasse diagram for the following partial order. Domain: {3, 5, 6, 7, 10, 14, 20, 30, 60}. x
Consider the partial order with domain {3, 5, 6, 7, 10, 14, 20, 30, 60} and with x ≤ y if x evenly divides y. Select the correct Hasse diagram for the partial order. Figure 2: A Hasse diagram shows a set of elements, 3, 5, 6, 7, 10, 14, 20, 30, and 60. The elements are arranged as follows: 3, 6, and 30 are arranged vertically one above another, connected by vertical line segments; 5 and 20 are arranged vertically one above another to the right of 3 and 6, respectively, connected by a vertical line segment; 10 is placed inclined up to the right of 20, horizontally aligned with 30, and 60 is placed above 30 and 10, vertically aligned with 20; at the top; inclined line segments connect 10 and 30, 30 and 60, 60 and 20, 20 and 5, 5 and 10, and 5 and 30 to form a diamond shape; and 7 and 14 are placed to the right of 5 and 10, respectively, connected by a vertical line segment.
Answer these questions for the partial order represented by the given Hasse diagram. b Find the least upper bound of (a, b, c), if it exists. (You must provide an answer before moving to the next part.) Multiple Choice с m no least upper bound
Part 2. Each relation given below is a partial order. Draw the Hasse diagram for the partial order. (a) The domain is {3, 5, 6, 7, 10, 14, 20, 30, 60}. x ≤ y if x evenly divides y. 1 (b) The domain is {a, b, c, d, e, f}. The relation is the set: {(b, e), (b, d), (c, a), (c, f), (a, f), (a, a), (b, b), (c, c), (d, d), (e, e), (ƒ, f)}
Part 2: Consider the partial order with domain {3, 5, 6, 7, 10, 14, 20, 30, 60, 70} and with r < y if r evenly divides y. Select the correct Hasse diagram for the partial order. 60 70 30 14 6 10 | 3 5 7 (b) Figure 3: 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, 10 and 70, 7 and 14, 14 and 70. 20
4. Let A := {1, 2, 3, 4} := B. (a) What is the cartesian product of A and B. (b) Find S := {(a, b)|f € Z}. (d) Is S a Partial Order? Justify your answer.
Which of the following relations is the a partial ordering on the set A = {3,7,9}? {(3,3),(7,7), (3,9),(9,7), (9,9)} O {(3,3),(7,7),(7,9),(9,9), (9,7)} O 3,3,7,7,9,9,3,7,7,9,3,9 O None of the others O {(3,3),(3,7),(7,9),(7,7),(9,9)}
A4. a. Draw a Digraph represented by the adjacency matrix 1 1 1 1 1 1 1 b. Consider the recurrent relationA, = 2An-1 + 3An-2, where n 2 2 and A = 1, A, = 2. Compute the next 4 terms (A2, A3, A4, A5) of the relation.

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What are the minimal elements of the partial order? What are the maximal elements of the partial order? Which of the following pairs are comparable? (A, D), (J. F). (B, E). (G, F). (D. B). (C, F). (H, I), (C. E)