Math 221 Discrete Mathematics UOPX I need week 4 of help all are listed below Make sure all of them are fresh work with proper citation APA format; no used work will be accepted thanks so much. ONLY Highlighted in Yellow Questions need to be answer. I need Help on my Discrete Math 221 for University of Phoenix Week 4 and Week 5 please take a look at my attachment I need week 4 class participation and on week 4 I need class participation, on Individual Assignment word 800-1250 essay assignments and student connect solutions. Please take a look its very small work not much. Book Name: Discrete Mathematics and Its Applications ,Seventh Edition by Kenneth Rosen instructor name: stephen wiitala for University of Phoenix Make sure while you write any of those answer please use it proper citations as you can see above red lines from my instructor he is very restrict about citations, I request you to read that and follow his instructions thanks so much. Week4 Graph Theory and Trees 1)The intersection graph of a collection of sets A1, A2, . . . , An is the graph that has a vertex for each of these sets and has an edge connecting the vertices representing two sets if these sets have a nonempty intersection. a) Upload the file for the following problem: Construct the intersection graph of these collections of sets: A1 = {0, 2, 4, 6, 8}, A2 = {0, 1, 2, 3, 4}, A3 = {1, 3, 5, 7, 9}, A4 = {5, 6, 7, 8, 9}, A5 = {0, 1, 8, 9} b) Upload the file for the following problem: Construct the intersection graph of these collections of sets: A1 = {. . . ,4,3,2,1, 0} A2 = {. . . ,2,1, 0, 1, 2, . . .} A3 = {. . . ,6,4,2, 0, 2, 4, 6, . . .} A4 = {. . . ,5,3,1, 1, 3, 5, . . .} A5 = {. . . ,6,3, 0, 3, 6, . . .} c) Upload the file for the following problem: Construct the intersection graph of these collections of sets: A1 = {x | x < 0} A2 = {x | 1 < x < 0} A3 = {x | 0 < x < 1} A4 = {x | 1 < x < 1} A5 = {x | x > 1} A6 = R 2) Consider the graph W4. Enter the elements of the adjacency matrix of the given graph. I have done one out of five so please help me other fours? 01011 10 1 0 1 01011 10101 11110 Class Discussions:- 2 questions Question 1: An Application of Graph Theory in Network Design Suppose that we have a communication network with 5 nodes, and each pair of nodes is connected directly. This network can be represented by a graph with 5 vertices {A,B,C,D,E}, and 10 edges {AB,AC,AD,AE,BC,BD,BE,CD,CE, DE}. Assume the the network has been hit with a disaster in such a a way that each link has a 50% probability that the link is intact. Simulate that situation by flipping a coin 10 times, once for each edge. If the coin is heads, the link has remaind intact. If the coin is tails, the link has been lost. 1. Draw the resulting graph 2. How many edges does the resulting graph have? 3. Is the graph that results connected? What does this mean for the ability to continue to communicate through the network? 4. Do you think that if a 6th node were added to the network but we were limited to having only 10 edges if the situation would change? How would you arrange the edges make it as likely as possible that the network would remain connected? This is actually a discussion related to an interesting topic in graph theory known as random graphs. This theory can explore the chances that various network configurations remain intact based on various probabilities of failures of links in the network (we might change the probability of a failure from 50% to some other value). Question 2: Trees and Computations Trees occur in various venues in computer science: decision trees in algorithms, search trees, and so on. One important kind of trees computer languages is the parse tree. It is used to break down statements in a programming langue into a form that can be converted into machine code. The most familiar of these kinds of trees are used to break down Arithmetic statements into trees. For example, the computation 2*3 + 4, can be parsed into the following tree + / \\ * 4 / \\ 2 3 On the other hand the computation 2 * (3 + 4) would have a different parse tree * / \\ 2 + / \\ 3 4 1. What are the similarities differences between the two trees in terms of depth, roots, and breadth? 2. What do those differences between the trees tell us about the differences between the steps need to do each computation. 3. Provide an arithmetic computation with at least three operations in it, and determine its parse tree. **I need week 4 Student connect express solutions please post that before. I will start working on the lab once you give me student connect express solutions. Thanks.**