# Discreet math homework/MAD 2104 â€“ ONLINE â€“ Spring 2017 Written Assignment 1 This assignment covers material from Module 1 Lesson 1-3

Discreet math homework/MAD 2104 â€“ ONLINE â€“ Spring 2017 Written Assignment 1 This assignment covers material from Module 1 Lesson 1-3

1. Let P, Q, and R be three statements. Determine if the following two statements are logically equivalent: P â†’ (Qâˆ§R) and (âˆ¼ Qâˆ¨âˆ¼ R) â†’âˆ¼ P You may use the following

table to organize your solution: [10 points]
P Q R âˆ¼ P âˆ¼ Q âˆ¼ R (Qâˆ§R) (âˆ¼ Qâˆ¨âˆ¼ R) P â†’ (Qâˆ§R) (âˆ¼ Qâˆ¨âˆ¼ R) â†’âˆ¼ P T T T T T F T F T T F F F T T F T F F F T F F F
2. Let P,Q,R,S be four mathematical statements. Suppose P is a false and (R â†’ S) â†” (P âˆ§Q) is a true statement, ï¬nd the truth values of R,S. [10 points] (This can be

done without a truth table.)
3. Consider the following statement and its proof. Whatâ€™s wrong with this proof?[10 points] â€œLet x and y be two positive numbers. If x â‰¤ y, then âˆšx â‰¤âˆšy.â€ Proof :

Suppose âˆšx â‰¤âˆšy. Taking the square of both sides, we get x â‰¤ y which is true. Therefore, âˆšx â‰¤âˆšy. 4. Negate the following statements (a) [5 points] The square of every

real number is non-negative. (b) [5 points] If âˆšx is a rational number, then x is not a prime number. (c) [5 points] The number x is even or the number y is even. (d)

[5 points] For every prime number p, there exists another prime number q with q > p.
5. Prove the following statements using direct proof.[10 points each] (a) If x is an even integer, then x2 âˆ’6x + 5 is odd. (Hint: The following is NOT a proof of this

statement: â€œLet x = 2, then x2 âˆ’6x + 5 = 22 âˆ’2Â·4 + 5 = 4âˆ’4 + 5 = 5 is odd.â€) (b) Suppose x,y âˆˆR. If x > y, then y3 + yx2 > x3 + xy2. (c) If n is an odd integer, then

n2 âˆ’1 is a multiple of 8. (d) Suppose that a, b, c are integers. Prove that if a2|b and b3|c, then a6|c. (e) If d is an integer with d > 2, then the equation x2 + 3x +

d = 0 has no real solution.
1
(f) If two integers have opposite parity, then their product is even. (Use formal deï¬nitions of odd and even numbers in your proof!)
2

# Our Service Charter

1. ### Excellent Quality / 100% Plagiarism-Free

We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers.
2. ### Free Revisions

We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed.
3. ### Confidentiality / 100% No Disclosure

We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service.
4. ### Money Back Guarantee

If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit.

We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.

Excellent Quality
Zero Plagiarism
Expert Writers

or