Order Discrete Math Assignment

Order Discrete Math Assignment
The University of Maine at Augusta Name: ________________________ Mathematics Department Date: ________________________ MAT 280 F16
MAT 280 Exam 2 Proofs
Please answer the following questions. You my use your book and other outside resources.
However, all work should represent the individual student’s efforts. This exam covers
primarily sections 1.7 and 1.8, however there will be some questions from 1.5 and 1.6.
1. Show that the premises, “ Arron is registered as an instate student” and “All instate students have permanent addresses in Maine” imply the conclusion “Arron’s permanent address is in Maine”
2. Determine whether the following argument is valid.
Rainy days make gardens grow.
Gardens don’t grow if it is not hot.
It always rains on a day that is not hot.
Therefore, if it is not hot, then it is hot.
3. What is the rule of inference used in the following:
If I work all week on this take home exam, then I can answer the questions correctly. If I
answer the questions correctly, I will pass the exam. Therefore, if I work all week on this take
home exam, then I will pass the exam.
4. Suppose you wish to prove a theorem of the form “if p then q”.
a. If you give a direct proof, what do you assume and what do you prove?
b. If you give an indirect proof, what do you assume and what do you prove?
c. If you give a proof by contradiction, what do you assume and what do you prove?
5. Suppose you are allowed to give either a direct proof or a proof by contraposition of the following: if 5n 3 is even, then n is odd.
a. Which type of proof would be easier to give, direct or indirect? Explain why.
b. Prove: If 5n 3 is even then n is odd.
6. In the following proof, name the proof technique:
Prove that p→q
Proof: Assume that p → q is true….. Proof continued…..
7. Prove: If x is odd, then 7 x – 4 is odd
1. Suppose x is odd. [Show 7x – 4 is odd .]
2. If x is odd then by definition, x = 2k 1, where k is an integer
⇒ 7x – 4 = 7( 2k 1) – 4 (substitution) = 14k 7 – 4
= 14k 3
=2(7k 1) 1
= 2m 1 is odd for integer m =7k 1
Therefore, 7 x – 4 is odd.
Which of the following applies? a. method of direct proof d. proof by contrapositive
b. method of indirect proof c. proof by contradiction
e. b and d
8. What is wrong with the following “proof” that -2 = 2, using backward reasoning?
Assume that -2 = 2. (-2)2 = 22 Squaring both sides
4 = 4 Therefore -2 = 2.
9. It is important to ask a key question when attempting to prove a statement. For the key question, “How can I show that 2 lines in a plane are perpendicular?” which of the following answer(s) is/are incorrect? Explain why.
a. Show that the product of the slopes of the two lines equal -1.
c. Show that the lines are on adjacent sides of a rectangle. d. None
b. Show that each of the lines is perpendicular to a third line.
10. In class we mentioned that Key questions help to give oneself direction when starting a proof.
Suppose you are asked to prove, “If a, b, and c are integers and ab and bc then ac”.
The symbol  means divides.
a. State a possible Key question that would help you to work through this proof.
b. Prove: If a, b, and c are integers and ab and bc then ac
11. Show that the statement ”The product of 2 irrational numbers is irrational” is false by finding a counterexample.
12. Given a class of 25 students prove that at least 4 of them were born on the same day of the week.
13. Give a direct proof of the following: “If m and n have different parities, then the sum of the m and n is odd”.
14. Give a proof by contradiction of the following: “If b is an odd integer, then b2 is odd”.
15. Prove: If a, b and c are even integers, then abc is divisible by 8.
16. Prove: If x and y are rational numbers then x divided by y is a rational number.
17. Prove or disprove that if m is an integer then 12
)3)(2)(1(  mmmm is an integer.
18. Prove: If a and b are integers with a ≠ 0 and x is a real number such that ax2 bx b – a = 0, then a│b.
Note: a│b means that a divides b or a is a factor of b.
19. Given that a and b are integers and a ≠ 0. Prove that if a|300 and a|(b 300), then a|b. (see number 14 for definition of a|b.)

Place your order
(550 words)

Approximate price: $22

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
The price is based on these factors:
Academic level
Number of pages
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more

Order your essay today and save 30% with the discount code HAPPY