Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. in this problem you will complete the details of t

In this problem you will complete the details of the proof of an if and...

70.2K

Verified Solution

Question

Basic Math

image

In this problem you will complete the details of the proof of an if and only if statement Fill in the blanks below Each blank should be filled with a polynomial in the variable k Prove Let n be an integer Then n is even if and only if n is even We will prove the following two statements 1 If n is even then n is even 2 If n is even then n is even Direct proof of 1 Suppose that n is even By definition n 2k for some integer k So n 2k 2m where m Since Z is closed under addition and multiplication me Z Since n 2m this means that n is even Indirect proof of 2 Suppose that n is even Assume for the sake of contradiction that n is odd Since n is odd n 2k 1 for some integer k This means that n 2k 1 4k 4k 1 2p 1 where p 8 Since Z is closed under addition and multiplication p E Z Since n is of the form 2p 1 for some integer p this means that n is odd However this contradicts the fact that n is even Therefore n must be even O

Answer & Explanation Solved by verified expert
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Basic Math
1.2K views

Gundy Company expects to produce 1 270 800 units of Product XX in 2020 Monthly...

Psychology
1.2K views

Please read and answer the question below. Quelling? ?Violence? ?in? ?Our? ?Country One? ?only? ?has? ?to? ?turn?...

Electrical Engineering
1.2K views

On the planet Mars, the power per unit area in sunlight is F = 590Wm-2 ....

Advance Math
1.2K views

The data is in the nonlinear regime. The first column is plastic strain values (e) and...

Biology
1.2K views

1 Describe what you would like to know more about video games 2 Explain why...

Biology
1.2K views

Where is this type of tissue found located 2 Under epithelia Most of the digestive...

Physics
1.2K views

The diagram shows a solenoid carrying time varying current I It I is constant On...

Basic Math
1.2K views

Solve the equation x + 9x - 30 using the Quadratic Formula.Give your answers as...

Accounting
1.2K views

the viner Wher: The actiation identifes ithe asset Mdind Telocen khoug meave the of this...

Accounting
1.2K views

ABC purchase three pieces of equipment from XYZ for $400,000. Given the following information, calculate...

Finance
1.2K views

You have $100,000 that you want to invest in a risky asset portfolio; M. Portfolio...

Accounting
1.2K views

Think about the sales and cash receipts process of a mens or womens clothing store...