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Hunter - Essentials of Discrete Mathematics 3/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 40 / 44

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7
20/20 6/6 2/4 7/7 0/1 5/5 0/1
Total
40/44 (90.9%)

  • Instructions

    Essentials of Discrete Mathematics, third edition, written by by David Hunter and published by Jones and Bartlett Learning, is designed to serve computer science and mathematics majors, as well as students from a wide range of other disciplines. The mathematical material is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. The WebAssign component of this text features an interactive eBook, diagrams, and randomized images.

    All questions include a link to the eBook.

    Question 1 has students fill in a Truth Table to establish one of De Morgan's laws.

    Questions 2 guides students to show given statements are true.

    Question 3 lets students enter any valid counterexample for each subpart.

    Question 4 uses a Tree Diagram so students can easily visualize the binary search.

    Question 5 grades the set of cross products and is flexible enough for students to enter elements in any order.

    Question 6 displays the five steps in a bottom-up construction of a Kgraph for students to explain.

    Question 7 asks students to count the number of rectangles in a randomized image that displays varying numbers of rows and columns.

    View the complete list of WebAssign questions available for this textbook.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 20/20 points  |  Previous Answers HunterDM3 1.1.010a. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100
Total
20/20
 
Use truth tables to establish the following equivalence.

Show that
¬(p ∨ q)
 is logically equivalent to
¬p ∧ ¬q.
 This equivalence is one of De Morgan's laws, after the nineteenth-century logician Augustus De Morgan.
p q ¬p ¬q p ∨ q ¬(p ∨ q) ¬p ∧ ¬q
T T Correct: Your answer is correct. seenKey

F

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F

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T

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F

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F
T F Correct: Your answer is correct. seenKey

F

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T

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T

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F

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F
F T Correct: Your answer is correct. seenKey

T

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F

 		Correct: Your answer is correct. seenKey

T

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F

 		Correct: Your answer is correct. seenKey

F
F F Correct: Your answer is correct. seenKey

T

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T

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F

 		Correct: Your answer is correct. seenKey

T

 		Correct: Your answer is correct. seenKey

T
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2. 6/6 points  |  Previous Answers HunterDM3 1.4.006a. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
1/1 1/1 1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100 1/100 1/100
Total
6/6
 
Consider the following definition of the "" symbol.
Definition. Let x and y be integers. Write x y if
5x + 2y = 3k
 for some integer k.
Show that
1 8,
2 1,
 and
0 3.
1 8 = 5 · (1) + 2 · 
 Correct: Your answer is correct. seenKey

8
 = 3 · 
 Correct: Your answer is correct. seenKey

7
2 1 = 5 · 
 Correct: Your answer is correct. seenKey

2
 + 2 · (1) = 3 · 
 Correct: Your answer is correct. seenKey

4
0 3 = 5 · (0) + 2 · 
 Correct: Your answer is correct. seenKey

3
 = 3 · 
 Correct: Your answer is correct. seenKey

2
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3. 2/4 points  |  Previous Answers HunterDM3 1.4.015. My Notes
Question Part
Points
Submissions Used
1 2 3 4
0/1 1/1 1/1 0/1
1/100 1/100 1/100 1/100
Total
2/4
 
Find a counterexample for each statement.
(a) If n is prime, then 2n − 1 is prime. (Enter an answer where n < 200.)
n =
4
Incorrect: Your answer is incorrect. webMathematica generated answer key


(b) Every triangle has at least one obtuse angle. (An angle is obtuse if it has measure greater than 90°.)
     Correct: Your answer is correct.

(c) For all real numbers x,
x2 ≥ x.
x =
0.5
Correct: Your answer is correct. webMathematica generated answer key


(d) For every positive nonprime integer n, if some prime p divides n, then some other prime q (with
q ≠ p)
 also divides n.
n =
22
Incorrect: Your answer is incorrect. webMathematica generated answer key
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4. 7/7 points  |  Previous Answers HunterDM3 2.1.024a. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
1/1 1/1 1/1 1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100 1/100 1/100 1/100
Total
7/7
 
Consider the following list of numbers.
129, 688, 126, 513, 605, 55, 46
Place the numbers, in the order given, into a binary search tree.
                 Correct: Your answer is correct. seenKey

129
                 slash back-slash
                                  Correct: Your answer is correct. seenKey

126

 		Correct: Your answer is correct. seenKey

688

 		                
                 slash slash                     
                 Correct: Your answer is correct. seenKey

55

 		                 Correct: Your answer is correct. seenKey

513

      		                
                     slash                  back-slash                 
     Correct: Your answer is correct. seenKey

46

 		                   Correct: Your answer is correct. seenKey

605

 		                
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5. 0/1 points  |  Previous Answers HunterDM3 2.2.016. My Notes
Question Part
Points
Submissions Used
1
0/1
1/100
Total
0/1
 
Write down all elements of
{H, I, J} × {N, O}.
 (Enter your answer in set notation.)
{HN, IN, JN, HO, IO, JO}
Incorrect: Your answer is incorrect. \big\{(H,N),(H,O),(I,N),(I,O),(J,N),(J,O)\big\}
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6. 5/5 points  |  Previous Answers HunterDM3 3.5.023. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
1/1 1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100 1/100
Total
5/5
 
Define a Kgraph as follows.
B. is a Kgraph.
R1. If is a Kgraph, so is . (Any edge can be bisected.)
R2. If is a Kgraph, so is . (Any two vertices can be joined.)
Give reasons (B, R1, or R2) for each of the following five steps in the bottom-up construction of a Kgraph.
Correct: Your answer is correct. seenKey

B

 		Correct: Your answer is correct. seenKey

R1

 		Correct: Your answer is correct. seenKey

R2

 		Correct: Your answer is correct. seenKey

R1

 		Correct: Your answer is correct. seenKey

R2
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7. 0/1 points  |  Previous Answers HunterDM3 4.3.006d. My Notes
Question Part
Points
Submissions Used
1
0/1
1/100
Total
0/1
 
The following figure consists of 8 horizontal lines and 13 vertical lines. The goal of this problem is to count the number of rectangles (squares are a kind of rectangle, but line segments are not).
WebAssign Plot
Let V be the set of all sets of two vertical lines, and let H be the set of all sets of two horizontal lines. Let R be the set of all rectangles in the figure. Define a function
f : R → V × H
 by
 
f
↦
 		({AB, CD}, {AC, BD}).
Compute |R|, the number of rectangles in the figure.
Incorrect: Your answer is incorrect. seenKey

2184
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