Find Jobs
Hire Freelancers

Discrete Mathematics

$30-40 AUD

In Progress
Posted over 3 years ago

$30-40 AUD

Paid on delivery
1. (5 %) (a) Use the laws of logic to simplify the statement ((p → ¬q) ∧ p) ∨ q. (b) Find the truth table for the statement (p ⊕ q) → (q ↑ r). 2. (5 %) (a) Write the following English sentences in predicate logic. The domains are forms of transport (bus/car/train/walk/...) used to get to university and students who use them. Make sure you define the predicates you use. i. Some students use the train to get to university. ii. Some students need to use two forms of transport to get to university. iii. Every student has some form of transport to get to university. iv. Some students cannot walk to university. (b) Given p(x, y) as ”x + y = 6” where x and y in the set {0,1,2,3,4,5,6}, determine whether the following are true or false. i. p(3,2) ii. ∀x, p(x, 1) iii. ∀x, ?x ̸= 0 → ∃y, p(x,y)? iv. ∃y, ∀x, p(x, y) 3. (5 %) Use a contrapositive proof to show, for integers a and b, that if ab is odd then a and b are odd. 4. (5 %) GiventhesetsA=Z5 ={0,1,2,3,4},B={2n:n∈Z}andC={x∈Z:−4<x<4}find: (a) A non-empty subset of B × (C − A) (b) P(C−B) (c) |A3 ×(B∩C)×C| (d) A∩(B∪C) 5. (5 %) Suppose that you had a simple connected graph with degree sequence 5,4,4,3,3,2,2,1 (a) Draw such a graph. Label the nodes A,B,C,D,E,F,G,H so that you can refer to them in later parts of this question. (b) Is it possible to find an Euler path or cycle for your graph? If so write down the path or cycle. If not, can you, by adding a single edge to your graph, create a new graph that does have an Euler path? If so, state clearly the edge and the resulting Euler path. If this is also not possible, explain why. (c) Is it possible to find a Hamiltonian cycle for your graph? If so write down the cycle. If not, can you, by adding a single edge to your graph, create a new graph that does have a Hamiltonian cycle? If so, state clearly the edge and the resulting Hamiltonian cycle. If this is also not possible, explain why. 6. (5 %) For this question consider the following two adjacency matrices, ABCDEFGH ABCDEFGH A00001110 A00110010 B00001110 B00011100 C00001111 C10001010 D00000001 D11001110 E11100000 E01110000 F11100010 F01010010 G11100101 G10110100 H00110010 H00000001 (a) Provide the associated graphs for both of these adjacency matrices. (b) Provide the degree sequences for both graphs. (c) Prove that one of the graphs is not planar, whilst the other graph is planar. (d) Explain why the graphs are not isomorphic. 7. (5 %) In this question we will look at a simple application of finding minimal spanning trees. Consider the graph below, which we will assume represents the distances between various towns. The government wants to lay wires to connect these towns in a network. However, digging trenches and laying wires is expensive, so the government wants to know the minimum cost of laying wire whilst still connecting all the places shown on the graph. The cost of laying wire (in thousands of dollars) between specific towns is shown next to each edge. Use Prim’s or Kruskal’s algorithm to construct a minimal spanning tree. State which algorithm you use, show the order in which edges are added, and state at the end what the minimum total cost is. 80 90 95 BCD 70 90 75 85 60 100 70 105 E F 90 G 90 H 85 65 70 85 55 85 105 150 65 90 IJKL 80 80 70 55 65 MN A 8. (5 %) Determine the chromatic numbers and chromatic polynomials for both of the graphs below. Hint: the graph on the right may require multiple steps for the chromatic polynomial.
Project ID: 27776768

About the project

5 proposals
Remote project
Active 3 yrs ago

Looking to make some money?

Benefits of bidding on Freelancer

Set your budget and timeframe
Get paid for your work
Outline your proposal
It's free to sign up and bid on jobs
Awarded to:
User Avatar
Discrete Mathematics I assure you quality work as per your given deadline. I can provide you with a guarantee of plagiarism free work. I am producing quality content for my clients including ARTICLE WRITING, ESSAY WRITING, RESEARCH PAPERS, BUSINESS PLAN, TECHNICAL WRITING, MATLAB, THESIS & DISSERTATIONS. I can provide your work as per your requirements along with free of cost changes facility. https://www.freelancer.com/u/PremiumSolution?w=f. Thanks
$35 AUD in 1 day
5.0 (5 reviews)
2.8
2.8
5 freelancers are bidding on average $45 AUD for this job
User Avatar
Hi, there I am interested in your project. I am an expert in Mathematics and Physics I have experiences in many fields. I can help you well. Kindly contact with me. Thanks.
$80 AUD in 2 days
5.0 (34 reviews)
5.2
5.2
User Avatar
Greetings sir, I am Irfan Marwat currently studying in Ph.D. Mathematics. My Research field is Algebra and Cryptography. I have been teaching Mathematics and Statistics for the last 6 years in different Educational institutions even at the university level. You Can Imagine how good I would be in Mathematics. Moreover, I have good knowledge of Statistical analysis too. On different freelancing platforms, I have been helping my clients for more than 4 years or so and I got great response and Admiration from them. I went through your project description. I got to know that You are requesting help regarding the Discrete Mathematics. Fortunately, I have been teaching Discrete Mathematics to Engineering students for the last 4 years. It is an interesting subject. Due to my self-study and Through the Teaching I got an excellent understanding and significant experience in these most important Mathematical tools. You can check samples of my work Related to your project on my profile. I have recently completed a project similar to your requested service can show you my previous work if needed. So If you are looking for a Mathematician and Statistician as well, Then I am the best choice for you over here. So do not miss this opportunity and get bless with my excellent and extremely accurate services. Thank you, Regards and Best wishes. Irfan Marwat
$35 AUD in 7 days
5.0 (15 reviews)
3.7
3.7
User Avatar
Hi, I am Saleh din i have master degree statistics and exprience data analysis, report writing, R, spss, and latex,data entry, word, python. I  do this job if give me that, done very  with best quality. 
$45 AUD in 3 days
5.0 (5 reviews)
1.8
1.8
User Avatar
Greeting, I have been done Ms in mathematics from school of mathematics Lahore pakistan.i have many project of mathmatics.i have lots of experience in all fields of math i will deliver premium quality work in the time. Thank you.
$30 AUD in 1 day
5.0 (4 reviews)
1.1
1.1

About the client

Flag of AUSTRALIA
MARSFIELD, Australia
5.0
12
Payment method verified
Member since Sep 19, 2019

Client Verification

Thanks! We’ve emailed you a link to claim your free credit.
Something went wrong while sending your email. Please try again.
Registered Users Total Jobs Posted
Freelancer ® is a registered Trademark of Freelancer Technology Pty Limited (ACN 142 189 759)
Copyright © 2024 Freelancer Technology Pty Limited (ACN 142 189 759)
Loading preview
Permission granted for Geolocation.
Your login session has expired and you have been logged out. Please log in again.