Show that the additive inverse, or negative, of an even number is an

1. Use a direct proof to show that the sum of two even integers is even.

3. Show that the additive inverse, or negative, of an even number is an even number using a direct proof.

4. Use a direct proof to show that the product of two odd numbers is odd.

5. Prove that if n is a perfect square, then n + 2 is not a perfect square.

6. Use a direct proof to show that the product of two rational numbers is rational.

7. Prove that if m and n are integers and mn is even, then m is even or n is even.

8. Prove that if n is an integer and 3n + 2 is even, then n is even using

a) a proof by contraposition

b) a proof by contradiction

9. Prove the proposition P(1), where P(n) is the proposition “If n is a positive integer, then n2 ≥ n”. What kind of proof did you use?

11. Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks.

12. Prove that if n is a positive integer, then n is even if and only if 7n + 4 is even.

13. Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers.

 

 

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:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency
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