5.For each of the following partial orders, draw a Hasse diagram, find themaximal and minimal elements, and determine whether the partial order is a total order.a. Ris a partial order on the set {0, 2, 4, 6,8, 10} such that (x, y) e R if and only if x y.b. Ris a partial order on the set {2, 3, 5, 9, 10, 11, 30} such that (x, y) E R if and only if x isdivisible by y. Hint: An integer x is divisible by an integer y with y + 0 if and only if thereexists an integer k such that x = yk.

(a) Given, R is a partial order on the set 0, 2, 4, 6, 8, 10 such that (x, y)∈R if…

Answered: 5. For each of the following partial…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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11./ a) b) c) 11 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 1 Determine if the relation is reflexive. If it is not reflexive, state why. Determine if the relation is symmetric. If it is not symmetric, state why. Sketch a digraph to represent the relation.
4. Use the tree rooted at A to answer the following questions. A K E L B M O H P D N Q R (a) List the order of the vertices produced by using Breadth-First Search. (b) List the order of the vertices produced by using Pre-Order Depth First Search. (c) List the order of the vertices produced by using Post-Order Depth First Search.
choose all the correct ones:
The drawing below shows a Hasse diagram for a partial order on the set {A, B, C, D, E, F, G, II, I, J} Figure 3: A Hasse diagram shous 10 vertices and 8 edges. The vertices, rep- resented by dots, are as follows: verter J; vertices II 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 II and I; vertex G is inclined upward to the right of vertex E; and vertex F is inclined downward to the right of vertex E. The edges, represented by line segments, between the vertices are as follows: Verter J is connected to no vertex; a vertical edge connects vertices II 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 B, Е аnd G, and E аnd P. (n) 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, E), (G, F),…
Draw the Hasse diagram for the following partial order. Domain: {3, 5, 6, 7, 10, 14, 20, 30, 60}. x
Please answer yes or no for each property.
part b and c
For any partial order there may be a number of linear orders that are consistent. For example,for the partial order (P (A), ⊂) with A = {1, 2, 3}, the ordering∅ ≺ {1} ≺ {2} ≺ {1, 2} ≺ {3} ≺ {1, 3} ≺ {2, 3} ≺ {1, 2, 3}does not violate the partial order, i.e. if a ≺ b → b ̸ ⊆ a. Find all the consistent linear orders for(P (A), ⊂) when A = {1, 2, 3, 4}.
11./ a) b) c) 11 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 1 Determine if the relation is reflexive. If it is not reflexive, state why. Determine if the relation is symmetric. If it is not symmetric, state why. Sketch a digraph to represent the relation.
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)}
1 1 1 c) The matrix M = 1 ㅇ represents the relations R defined 1 1 L1 0 0 1. the set A = {1, 2, 3, 4}. i) List the ordered pairs in the relation R. i) Draw the graph representing the relation R. d) How many edges does a 50–regular graph with 100 vertices have?

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5. For each of the following partial orders, draw a Hasse diagram, find the maximal and minimal elements, and determine whether the partial order is a total order.