Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Chapter 1.2, Problem 1TFQ
Two statements A and B are logically equivalent precisely when the statement
A
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Please answer exercise 11.2.10 and 11.4.1 stepwise
To help consumers in purchasing a laptop computef, Consumer Reports calculates an overall
test score for each computer tested based upon rating factors such as ergonomics, portability,
performance, display, and battery life. Higher overall scores indicate better test results. The
following data show the average retail price and the overall score for ten 13-inch models
(Consumer Reports website, October 25, 2012).
Price
Overall
Brand & Model
Score
Samsung Ultrabook NP900X3C-A01US
1250
83
Apple MacBook Air MC965LL/A
1300
83
Apple MacBook Air MD231LL/A
1200
82
HP ENVY 13-2050nr Spectre XT
950
79
Sony VAIO SVS13112FXB
800
77
Acer Aspire S5-391-9880 Ultrabook
1200
74
Apple MacBook Pro MD101LL/A
1200
74
Apple MacBook Pro MD313LL/A
1000
73
Dell Inspiron 113Z-6591SLV
700
67
600
63
Samsung NP535U3C-A01US
a. Develop a scatter diagram with price as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship
between the two variables?
c. Use the…
Please answer exercises 11.4.8 and 11.4.10 Stepwise
Chapter 1 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 1.1 - True/False Questions
“” means “”
Ch. 1.1 - A truth table based on four simple statements...Ch. 1.1 - True/False Questions
2. If is true, then is also...Ch. 1.1 - If p and q are both false, the truth value of...Ch. 1.1 - If pq is false, the truth value of (pq)(pq) is...Ch. 1.1 - pq andqp are logically equivalent.Ch. 1.1 - True/False Questions
7. A statement and its...Ch. 1.1 - (pq)(pq) is a tautology.Ch. 1.1 - True/False Questions
9. If B is a tautology and A...Ch. 1.1 - True/False Questions
10. If A and B are both...
Ch. 1.1 - Construct a truth table for each of the following...Ch. 1.1 - (a) If pq is false, determine the truth value of...Ch. 1.1 - 3. Determine the truth value for
when are all...Ch. 1.1 - 4. Repeat Exercise 3 in the case where are all...Ch. 1.1 - 5. (a) Show that is a tautology.
(b) Show that ...Ch. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - 10. (a) Show that the statement is not logically...Ch. 1.1 - 11. If and are statements, then the compound...Ch. 1.2 - True/False Questions
Two statements A and B are...Ch. 1.2 - True/False Questions
2. “A B” and “A B” mean the...Ch. 1.2 - True/False Questions
3. () () for any statement ....Ch. 1.2 - True/False Questions
4. for any statements
Ch. 1.2 - (p(qr))((pq)(pr)) for any statements p,q,r.Ch. 1.2 - ((pq))((p)(q)) for any statements p,q.Ch. 1.2 - If A Band C is any statement, then (A C) (B ...Ch. 1.2 - True/False Questions
8. is in disjunctive normal...Ch. 1.2 - (pq(r))((p)(q)(r)) is in disjunctive normal form.Ch. 1.2 - True/False Questions
10. Disjunctive normal form...Ch. 1.2 - Prob. 1ECh. 1.2 - (a) Show that p[(pq)] is a tautology. (b) What is...Ch. 1.2 - Simplify each of the following statements. (a)...Ch. 1.2 - 4. Using truth tables, verify the following...Ch. 1.2 - 5. Using the properties in the text together with...Ch. 1.2 - Prove that the statements (p(q))q and (p(q))p are...Ch. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Express each of the following statements in...Ch. 1.2 - Find out what you can about Augustus De Morgan and...Ch. 1.3 - True/False Questions
An argument is valid if,...Ch. 1.3 - Prob. 2TFQCh. 1.3 - Prob. 3TFQCh. 1.3 - True/False Questions
4. De Morgan’s laws are two...Ch. 1.3 - The chain rule has pq and qr as its premises.Ch. 1.3 - Prob. 6TFQCh. 1.3 - Prob. 7TFQCh. 1.3 - Prob. 8TFQCh. 1.3 - Prob. 9TFQCh. 1.3 - Prob. 10TFQCh. 1.3 - Determine whether or not each of the following...Ch. 1.3 - 2. Verify that each of the five rules of inference...Ch. 1.3 - Verify that each of the following arguments is...Ch. 1.3 - Test the validity of each of the following...Ch. 1.3 - 5. Determine the validity of each of the following...Ch. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - 10. What language is being used when we say “modus...Ch. 1 - Construct a truth table for the compound statement...Ch. 1 - Determine the truth value of [p(q((r)s))](rt),...Ch. 1 - 3. Determine whether each statement is a...Ch. 1 - Two compound statements A and B have the property...Ch. 1 - 5. (a) Suppose A, B, and C are compound statements...Ch. 1 - Establish the logical equivalence of each of the...Ch. 1 - 7. Express each of the following statements in...Ch. 1 - Determine whether each of the following arguments...Ch. 1 - Discuss the validity of the argument pq(p)r Purple...Ch. 1 - 10. Determine the validity of each of the...
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- Please answer exercises 11.4.4 and 11.4.5 Stepwisearrow_forwardData on advertising expenditures and revenue (in thousands of dollars) for the Four Sea- sons Restaurant follow, Advertising Expenditures Revenue 124 19 32 44 6 40 10 52 14 20 53 54 a. Let x equal advertising expenditures and y equal revenue. Use the method of least squares to develop a straight line approximation of the relationship between the two variables. b. Test whether revenue and advertising expenditures are related at a .05 level of significance. - C. Prepare a residual plot of yŷ versus ŷ. Use the result from part (a) to obtain the values of ŷ. d. What conclusions can you draw from residual analysis? Should this model be used, or should we look for a better one?arrow_forwardPlease answer exercises 11.2.7 and 11.2.8 Stepwisearrow_forward
- In a manufacturing process the assembly line speed (feet per minute) was thought to af- fect the number of defective parts found during the inspection process. To test this theory, managers devised a situation in which the same batch of parts was inspected visually at a variety of line speeds. They collected the following data. Line Speed 20 Number of Defective Parts Found 21 20 19 40 *** 40 15 30 16 60 14 17 a. Develop the estimated regression equation that relates line speed to the number of defective parts found. b. At a .05 level of significance, determine whether line speed and number of defective parts found are related. C. Did the estimated regression equation provide a good fit to the data? d. Develop a 95% confidence interval to predict the mean number of defective parts for a line speed of 50 feet per minute.arrow_forwardPlease answer exercise 11.4.11 Stepwisearrow_forwardIn exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4. - Room Rate Entertainment City ($) ($) Boston 148 161 Denver 96 105 Nashville 91 101 New Orleans 110 142 Phoenix 90 100 San Diego 102 120 San Francisco 136 167 San Jose 90 140 Tampa 82 98 a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89. b. Develop a 95% confidence interval for the mean amount spent on entertainment for C. all cities that have a daily room rate of $89. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago.arrow_forward
- Please answer exercises 11.4.6 and 11.4.7 Stepwisearrow_forwardAn important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume (units) 400 Total Cost ($) 450 550 600 700 750 4000 5000 5400 5900 6400 7000 a. Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. b. What is the variable cost per unit produced? c. Compute the coefficient of determination. What percentage of the variation in total cost can be explained by production volume? d. The company's production schedule shows 500 units must be produced next month. Predict the total cost for this operation?arrow_forwardPlease answer exercises 11.4.2 and 11.4.3 Stepwisearrow_forward
- Please answer exercise 11.2.5 and 11.2.6 stepwisearrow_forwardFind two unit vectors orthogonal to both given vectors. (7, -7, 7), (0, 2, 2) (smaller i-value) (larger i-value) Need Help? Read It Master Itarrow_forward(a) Let P be a point not on the line L that passes through the points Q and R. Show that the distance d from the point P to the line L is |a × b| |a| d where a QR and b QR and b = QP. = This answer has not been graded yet. (b) Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 7, 6) and R(-1, 2, 6).arrow_forward
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