Math proofs

1. Suppose that x2y + xy2 + y3 = x3:

a) Using the method of proof by contrapositive, show that if x and y are not both zero, then y ≠ 0.

Don't use plagiarized sources. Get Your Custom Essay on
Math proofs
Get an essay WRITTEN FOR YOU, Plagiarism free, and by an EXPERT!
Order Essay

b) Using the method of proof by contradiction, show that if x and y are not both zero, then y ≠ 0.

2. Prove the following two statements:

a) For every integer n, 72 | n iff 8 | n and 9 | n.

b) It is not true that for every integer n, 90 | n iff 6 | n and 15 | n.

3. Let a, b, and c be real numbers with a ≠ 0. Prove that limx→c (ax + b) = ac + b.

4. Suppose that {Ai | i ∈ I} is an indexed family of sets and B is a set. Prove that
(∩i∈I Ai) × B = ∩i∈I (Ai × B).

5. Suppose R is a partial order on A and S is a partial order on B. Define a relation T on A × B such that (a1, b1) T (a2, b2) iff a1 R a2 and b1 S b2. Is T a partial order on A x B? Either provide a proof to show that this is true or provide a counterexample to show that this is false.

Homework Sharks
Order NOW For A 10% Discount!
Pages (550 words)
Approximate price: -

Our Advantages

Plagiarism Free Papers

All our papers are original and written from scratch. We will email you a plagiarism report alongside your completed paper once done.

Free Revisions

All papers are submitted ahead of time. We do this to allow you time to point out any area you would need revision on, and help you for free.


A title page preceeds all your paper content. Here, you put all your personal information and this we give out for free.


Without a reference/bibliography page, any academic paper is incomplete and doesnt qualify for grading. We also offer this for free.

Originality & Security

At Homework Sharks, we take confidentiality seriously and all your personal information is stored safely and do not share it with third parties for any reasons whatsoever. Our work is original and we send plagiarism reports alongside every paper.

24/7 Customer Support

Our agents are online 24/7. Feel free to contact us through email or talk to our live agents.

Try it now!

Calculate the price of your order

We'll send you the first draft for approval by at
Total price:

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

We work around the clock to see best customer experience.


Flexible Pricing

Our prces are pocket friendly and you can do partial payments. When that is not enough, we have a free enquiry service.


Admission help & Client-Writer Contact

When you need to elaborate something further to your writer, we provide that button.


Paper Submission

We take deadlines seriously and our papers are submitted ahead of time. We are happy to assist you in case of any adjustments needed.


Customer Feedback

Your feedback, good or bad is of great concern to us and we take it very seriously. We are, therefore, constantly adjusting our policies to ensure best customer/writer experience.