(solution) please read carefully and finish on time if you have no

please read carefully and finish on time if you have no confidence to finish it, then don't pick it up

Homework 3 CSE 191 Fall 2016 Due: Friday 10/7/2016

 

This assignment has some examples of different proof methods as well as problems regarding set

 

notation. There are a total of 100 points on the assignment.

 

(1) (8 points) Prove that there is no positive integer n such that:

 

200 < (n + 1)2n < 300

 

Hint: try a proof by cases.

 

(2) (8 points) Prove or disprove the following statement:

 

If a and b are rational numbers then ab is a rational number.

 

(3) An integer m is a multiple of an integer a if there exists an integer k such that m = ak.

 

E.g., m is a multiple of 2 if there exists an integer c such that m = 2c.

 

E.g., m is a multiple of 5 if there exists an integer d such that m = 5d.

 

(8 points) Prove that if n2 is a multiple of 5, then n is a multiple of 5.

 

?

 

(4) (8 points)

 

Prove

 

that

 

5 is not a rational number. (hint: look at how the book/lecture

 

?

 

shows 2 is not rational)

 

(5) Let A, B, C, and D be the following sets:

 

A = {1, 2, 3, 4}

 

B = {1, 1, 3}

 

C = {1, {3}, 1, {1, 3}, {3, 3, 1}, {{1, 3}}}

 

D = {2, 2, 2, 3, 3, 4}

 

Provide the answer to the following questions about the above sets, providing a short

 

justification for each (1+1 points each, for a total of 32 points).

 

(5a) Is B ? A?

 

(5b) Is B ? C?

 

(5c) Is B ? D?

 

(5d) What is |A|?

 

(5e) What is |B|?

 

(5f) What is |C|?

 

(5g) What is |D|?

 

(5h) Is B ? A?

 

(5i) Is B ? C? (5j) What is A ? C?

 

(no justification needed for (5j))

 

(5k) What is A ? C?

 

(no justification needed for (5k))

 

(5l) What is B × D?

 

(no justification needed for (5l))

 

(5m) What is P(B)?

 

(no justification needed for (5m))

 

(5n) Is B ? P(C)?

 

(5o) Give a partition of A by 3 sets.

 

(5p) Does a partition of B by 3 sets exist? (6) For each of the following statements, state if it is always true for any two set s A and B. If

 

the statement is not always true, provide a counter example (4 points each, for a total of

 

20 points).

 

(6a) If A ? B, then A ? B.

 

(6b) If A ? B, then A ? B.

 

(6c) If A = B, then A ? B.

 

(6d) If A = B, then A ? B.

 

(6e) For any two sets, A and B, if A ? B, then A2 ? B2

 

(7) Using the set identities in section 3.5 of the zyBook, name the set identity used to justify

 

each of the identities given below (2 points each, for a total of 10 points)

 

(7a) (B ? C) ? (B ? C) = U

 

(7b) A ? (A ? B) = A

 

(7c) A ? (B ? C) = A ? (B ? C)

 

(7d) (B ? A) ? (B ? A) = (B ? A)

 

(7e) ((A ? B) ? C) ? ? = ?

 

(8) Prove or disprove that ? = {?}. (6 points)

 

---

Solution details:

About this Question

STATUS

Answered

QUALITY

Approved

DATE ANSWERED

Sep 13, 2020

EXPERT

Tutor

ANSWER RATING

GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

• As a reference for in-depth understanding of the subject.
• As a source of ideas / reasoning for your own research (if properly referenced)
• For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).

This we believe is a better way of understanding a problem and makes use of the efficiency of time of the student.

NEW ASSIGNMENT HELP?

Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions. New orders are original solutions and precise to your writing instruction requirements. Place a New Order using the button below.

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN A DEADLINE.