Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Textbook Question
Chapter 3.5, Problem 15E
Construct a valid argument based on the Euler diagram shown.
x represents Erin.
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answer number 4
3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
answer number 6
Chapter 3 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 3.1 - Decide whether each is a statement or is not a...Ch. 3.1 - The ZIP code for Oscar, Louisiana, is 70762.Ch. 3.1 - 3. Listen, my children, and you shall hear of the...Ch. 3.1 - 4.Did you yield to oncoming traffic?Ch. 3.1 - 5.
Ch. 3.1 - 6.
Ch. 3.1 - 7 Some numbers are positive.
Ch. 3.1 - |8. Grover Cleveland was president of the United...Ch. 3.1 - Accidents are the main cause of deaths of children...Ch. 3.1 - 10 It is projected that in the United States...
Ch. 3.1 - Where are you going tomorrow?Ch. 3.1 - Behave yourself and sit down.Ch. 3.1 - Kevin Catfish" McCarthy once took a prolonged...Ch. 3.1 - 14 One gallon of milk weighs more than 3 pounds.
Ch. 3.1 - Decide whether each statement is compound. I read...Ch. 3.1 - My brother got married in Copenhagen.Ch. 3.1 - 17. Tomorrow is Saturday.
Ch. 3.1 - Jing is younger than 18 years of age, and so is...Ch. 3.1 - Prob. 19ECh. 3.1 - 20. The sign on the back of the car read "Canada...Ch. 3.1 - 21 If Lorri sells her quota, then Michelle will be...Ch. 3.1 - If Bobby is a politician, then Mitch is a crook.Ch. 3.1 - Write a negation for each statement.
23. Her...Ch. 3.1 - 24. No rain fell in southern California today.
Ch. 3.1 - Some books are longer than this book.Ch. 3.1 - 26. All students present will get another chance.
Ch. 3.1 - 27. No computer repairman can play blackjack.
Ch. 3.1 - 28. Some people have all the luck.
Ch. 3.1 - Everybody loves somebody sometime.Ch. 3.1 - Prob. 30ECh. 3.1 - The trash needs to be collectedCh. 3.1 - Prob. 32ECh. 3.1 - Give a negation of each inequality. Do not use a...Ch. 3.1 - Prob. 34ECh. 3.1 - 35.
Ch. 3.1 - Prob. 36ECh. 3.1 - Try to negate the sentence The exact number of...Ch. 3.1 - Prob. 38ECh. 3.1 - Let p represent the statement 'She has green eyes...Ch. 3.1 - 40.
Ch. 3.1 - Prob. 41ECh. 3.1 - 42.
Ch. 3.1 - pqCh. 3.1 - 44.
Ch. 3.1 - pqCh. 3.1 - pqCh. 3.1 - (pq)Ch. 3.1 - 48.
Ch. 3.1 - Tyler collects DVDs and Josh is not an art major.Ch. 3.1 - Tyler does not collect DVDs or Josh is not an art...Ch. 3.1 - Tyler does not collect DVDs or Josh is an art...Ch. 3.1 - Josh is an art major and Tyler does not collect...Ch. 3.1 - 53. Neither Tyler collects DVDs nor Josh is an art...Ch. 3.1 - 54. Either Josh is an art major or Tyler collects...Ch. 3.1 - Incorrect use of quantifiers often is heard in...Ch. 3.1 - Prob. 56ECh. 3.1 - Refer to the groups of art labeled A. B. and C,...Ch. 3.1 - 58. No picture has a frame.
Ch. 3.1 - 59. At least one picture does not have a frame
Ch. 3.1 - Not every picture has a frame.Ch. 3.1 - 61. At least one picture has a frame.
Ch. 3.1 - 62. No picture does not have a frame.
Ch. 3.1 - All pictures do not have frames.Ch. 3.1 - Not every picture does not have a frameCh. 3.1 - 65. Every whole number is an integer.
Ch. 3.1 - 66. Every integer is a whole number.
Ch. 3.1 - There exists a natural number that is not an...Ch. 3.1 - 68. There exists an integer that is not a natural...Ch. 3.1 - 69. All rational numbers are real numbers.
Ch. 3.1 - Prob. 70ECh. 3.1 - Some rational numbers are not integers.Ch. 3.1 - Some whole numbers are not rational numbers.Ch. 3.1 - 73. Each whole number is a positive number.
Ch. 3.1 - Each rational number is a positive number.Ch. 3.1 - 75. Explain the difference between the statements...Ch. 3.1 - Prob. 76ECh. 3.1 - 77. Write the following statement using “every”:...Ch. 3.1 - Prob. 78ECh. 3.1 - Refer to Example 5. If we let c represent cat and...Ch. 3.1 - 80. Use symbols to express the statements for...Ch. 3.2 - 1. If q is false, what must be the truth value of...Ch. 3.2 - If q is true, what must be the truth value of the...Ch. 3.2 - If the statement pq is true, and p is true, then q...Ch. 3.2 - If the statement pq is false, and p is false, then...Ch. 3.2 - 5. If is true, what must be the truth value of...Ch. 3.2 - If p(qr) is true, what must be the truth value of...Ch. 3.2 - If (pq) is true, what must be the truth values of...Ch. 3.2 - If (pq) is false, what must be the truth values of...Ch. 3.2 - pCh. 3.2 - qCh. 3.2 - 11.
Ch. 3.2 - 12.
Ch. 3.2 - 13.
Ch. 3.2 - 14.
Ch. 3.2 - pqCh. 3.2 - pqCh. 3.2 - 17.
Ch. 3.2 - 18.
Ch. 3.2 - [p(p)]Ch. 3.2 - [(pq)q]Ch. 3.2 - 21. Is the statement a conjunction or a...Ch. 3.2 - Prob. 22ECh. 3.2 - Let p represent a true statement, and let q and r...Ch. 3.2 - 24.
Ch. 3.2 - p(qr)Ch. 3.2 - 26
Ch. 3.2 - (pq)(rq)Ch. 3.2 - (rq)(rq)Ch. 3.2 - 29.
Ch. 3.2 - [r(qp)]Ch. 3.2 - [q(rp)]Ch. 3.2 - 32.
Ch. 3.2 - Let p represent the statement 168. let q represent...Ch. 3.2 - Prob. 34ECh. 3.2 - qrCh. 3.2 - Prob. 36ECh. 3.2 - (pq)rCh. 3.2 - Prob. 38ECh. 3.2 - (rq)pCh. 3.2 - Prob. 40ECh. 3.2 - Give the number of rows in the truth table for...Ch. 3.2 - Prob. 42ECh. 3.2 - 43.
Ch. 3.2 - 44.
Ch. 3.2 - 45.
Ch. 3.2 - [(pq)(rs)][(mn)(uv)]Ch. 3.2 - 47 If the truth table for a certain compound...Ch. 3.2 - Is it possible for the truth table of a compound...Ch. 3.2 - Construct a truth table for each compound...Ch. 3.2 - pqCh. 3.2 - 51.
Ch. 3.2 - pqCh. 3.2 - (qp)qCh. 3.2 - 54.
Ch. 3.2 - 55.
Ch. 3.2 - (pq)(pq)Ch. 3.2 - (pq)rCh. 3.2 - r(pq)Ch. 3.2 - 59.
Ch. 3.2 - (rp)(pq)Ch. 3.2 - Construct a truth table for each compound...Ch. 3.2 - (rs)(pq)Ch. 3.2 - Use one of De Morgan’s laws to write the negation...Ch. 3.2 - I am not going or she is going.Ch. 3.2 - It is summer and there is no snow.Ch. 3.2 - Prob. 66ECh. 3.2 - I said yes but she said noCh. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - 810or52Ch. 3.2 - Prob. 71ECh. 3.2 - 72. The lawyer and the client appeared in court.
Ch. 3.2 - Prob. 73ECh. 3.2 - Prob. 74ECh. 3.2 - There exists an integer n such that n0andn0 ..Ch. 3.2 - 76. For some integer .
Ch. 3.2 - Complete the truth table for exclusive disjunction...Ch. 3.2 - Prob. 78ECh. 3.2 - Prob. 79ECh. 3.2 - Prob. 80ECh. 3.2 - Prob. 81ECh. 3.2 - Prob. 82ECh. 3.2 - Prob. 83ECh. 3.2 - Prob. 84ECh. 3.2 - 85 De Morgan's law
can be stated verbally, "The...Ch. 3.3 - Rewrite each statement using the if . . . then...Ch. 3.3 - Rewrite each statement using the if then...Ch. 3.3 - Rewrite each statement using the if . . . then...Ch. 3.3 - No perfect square integers have units digit 2, 3,...Ch. 3.3 - Prob. 5ECh. 3.3 - Rewrite each statement using the if then...Ch. 3.3 - Prob. 7ECh. 3.3 - Rewrite each statement using the if then...Ch. 3.3 - Prob. 9ECh. 3.3 - Decide whether each statement is true or...Ch. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Decide whether each statement is true or...Ch. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - |17. Explain why the statement “If , then ” is...Ch. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Let s represent “She sings for a living,” let p...Ch. 3.3 - Let s represent She sings for a living, let p...Ch. 3.3 - Prob. 27ECh. 3.3 - Let s represent She sings for a living, let p...Ch. 3.3 - Prob. 29ECh. 3.3 - Let s represent “She sings for a living,” let p...Ch. 3.3 - Prob. 31ECh. 3.3 - Let b represent I take my ball, lets represent it...Ch. 3.3 - Prob. 33ECh. 3.3 - Let b represent I take my ball, lets represent it...Ch. 3.3 - Prob. 35ECh. 3.3 - Let b represent I take my ball, lets represent it...Ch. 3.3 - Prob. 37ECh. 3.3 - Find the truth value of each statement. Assume...Ch. 3.3 - Prob. 39ECh. 3.3 - Find the truth value of each statement. Assume...Ch. 3.3 - Prob. 41ECh. 3.3 - Find the truth value of each statement. Assume...Ch. 3.3 - Prob. 43ECh. 3.3 - Find the truth value of each statement. Assume...Ch. 3.3 - Prob. 45ECh. 3.3 - Find the truth value of each statement. Assume...Ch. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Construct a truth table for each statement....Ch. 3.3 - Prob. 51ECh. 3.3 - Construct a truth table for each statement....Ch. 3.3 - Prob. 53ECh. 3.3 - Construct a truth table for each statement....Ch. 3.3 - Construct a truth table /breach statement....Ch. 3.3 - Construct a truth table /breach statement....Ch. 3.3 - Prob. 57ECh. 3.3 - Construct a truth table /breach statement....Ch. 3.3 - 59. What is the minimum number of Fs that must...Ch. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Write the negation of each statement. Remember...Ch. 3.3 - Prob. 63ECh. 3.3 - Write the negation of each statement. Remember...Ch. 3.3 - Prob. 65ECh. 3.3 - Write the negation of each statement. Remember...Ch. 3.3 - Write each statement as an equivalent statement...Ch. 3.3 - Prob. 68ECh. 3.3 - Prob. 69ECh. 3.3 - Prob. 70ECh. 3.3 - Prob. 71ECh. 3.3 - Prob. 72ECh. 3.3 - Prob. 73ECh. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Prob. 76ECh. 3.3 - Prob. 77ECh. 3.3 - Prob. 78ECh. 3.3 - Prob. 79ECh. 3.3 - Prob. 80ECh. 3.3 - Prob. 81ECh. 3.3 - Prob. 82ECh. 3.3 - Prob. 83ECh. 3.3 - Write a logical statement representing each of the...Ch. 3.3 - Write a logical statement representing each of the...Ch. 3.3 - Prob. 86ECh. 3.3 - Prob. 87ECh. 3.3 - Prob. 88ECh. 3.3 - Prob. 89ECh. 3.3 - Prob. 90ECh. 3.3 - Draw circuits representing the following...Ch. 3.3 - Prob. 92ECh. 3.3 - Prob. 93ECh. 3.3 - Draw circuits representing the following...Ch. 3.3 - Prob. 95ECh. 3.3 - Prob. 96ECh. 3.3 - Prob. 97ECh. 3.4 - For each given conditional statement (or statement...Ch. 3.4 - For each given conditional statement (or statement...Ch. 3.4 - If it aint broke, dont fix it. For each given...Ch. 3.4 - Prob. 4ECh. 3.4 - For each given conditional statement (or statement...Ch. 3.4 - 6, Milk contains calcium. For each given...Ch. 3.4 - For each given conditional statement (or statement...Ch. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - For each given conditional statement (or statement...Ch. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - 17 Discuss the equivalences that exist among a...Ch. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Write each statement in the form if p, then q....Ch. 3.4 - Prob. 23ECh. 3.4 - Write each statement in the form “if p, then...Ch. 3.4 - Write each statement in the form “if p, then...Ch. 3.4 - 26. Being in Kalamazoo is sufficient for being in...Ch. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - 30. The economy will recover only if employment...Ch. 3.4 - Prob. 31ECh. 3.4 - No integers are irrational numbersCh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - 36. A square is a rectangle with two adjacent...Ch. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - Prob. 53ECh. 3.4 - This number is positive. This same number is a...Ch. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.4 - Exercises 57 and 58 refer to the chapter opener on...Ch. 3.4 - Exercises 57 and 58 refer to the chapter opener on...Ch. 3.5 - Decide whether each argument is valid or...Ch. 3.5 - 2. All disc jockeys play music.
Ch. 3.5 - All celebrities have problems....Ch. 3.5 - All Southerners speak with an accent....Ch. 3.5 - All dogs love to bury bones...Ch. 3.5 - 6 All vice presidents use cell phones.
Ch. 3.5 - 7 All residents of Colorado know how to breathe...Ch. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - 10. Some philosophers are absent minded.
Ch. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - Refer to Example 3. If the second premise and the...Ch. 3.5 - Prob. 14ECh. 3.5 - Construct a valid argument based on the Euler...Ch. 3.5 - x represents vaccinationsCh. 3.5 - As mentioned in the text, an argument can have a...Ch. 3.5 - All actors have cars....Ch. 3.5 - All chickens have beaks....Ch. 3.5 - All chickens have beaks....Ch. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - 24. A scalene triangle has a longest side.
Ch. 3.5 - In Exercises 25-30. the premises marked A, B and C...Ch. 3.5 - 26. Some people who live in a suburb drive.
Ch. 3.5 - Prob. 27ECh. 3.5 - Some people who contribute to air pollution live...Ch. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.6 - Each argument either is valid by one of the forms...Ch. 3.6 - 2. If you use binoculars, then you get a glimpse...Ch. 3.6 - 3. If Marina works hard enough, she will get a...Ch. 3.6 - If Isaiahs ankle heals on time, hell play this...Ch. 3.6 - 5. If he doesn't have to get up at 3 00 a m., he's...Ch. 3.6 - A mathematician is a device for turning coffee...Ch. 3.6 - If Clayton pitches, the Dodgers win....Ch. 3.6 - If Josh plays, the opponent gets shut out....Ch. 3.6 - If youre going through hell, keep going. (quote...Ch. 3.6 - If you can't get rid of the skeleton in your...Ch. 3.6 - She uses e-commerce or she pays by credit card....Ch. 3.6 - 12 Mia kicks or Drew passes.
Ch. 3.6 - Use a truth table to determine whether the...Ch. 3.6 - pqp qCh. 3.6 - pqq pCh. 3.6 - Prob. 16ECh. 3.6 - 17.
Ch. 3.6 - 18.
Ch. 3.6 - 19.
Ch. 3.6 - 20.
Ch. 3.6 - 21. =
Ch. 3.6 - (pq)(pq)qpCh. 3.6 - (pq)(pq)p qCh. 3.6 - Prob. 24ECh. 3.6 - 25.
Ch. 3.6 - Prob. 26ECh. 3.6 - Earlier we showed how to analyze arguments using...Ch. 3.6 - Prob. 28ECh. 3.6 - Determine whether each argument is valid or...Ch. 3.6 - 30. If Hurricane Gustave hit that grove of trees,...Ch. 3.6 - 31. If Yoda is my favorite Star Wars character,...Ch. 3.6 - 32 Carne Underwood sings or Joe Jonas is not a...Ch. 3.6 - The Cowboys will make the playoffs if and only if...Ch. 3.6 - If I've got you under my skin. then you are deep...Ch. 3.6 - 35. If Dr. Hardy is a department chairman, then he...Ch. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - All men are mortal Socrates is a man Therefore,...Ch. 3.6 - A recent DirecTV commercial had the following...Ch. 3.6 - Molly made the following observation If I want to...Ch. 3.6 - Prob. 41ECh. 3.6 - 42. None of your sons can do logic.
Ch. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Let p be one is able to do logic," q be one is fit...Ch. 3.6 - Prob. 51ECh. 3.6 - Let p be it is a guinea pig. q be it is hopelessly...Ch. 3.6 - Prob. 53ECh. 3.6 - Prob. 54ECh. 3 - Write a negation for each statement. 63=3Ch. 3 - Write a negation for each statement. All men are...Ch. 3 - Prob. 3TCh. 3 - Write a negation for each statement. If I fall in...Ch. 3 - Write a negation for each statement.
5. She...Ch. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Using the same statements as for Exercises 6-8,...Ch. 3 - Prob. 10TCh. 3 - In each of the following assume that p is true and...Ch. 3 - In each of the following assume that p is true and...Ch. 3 - In each of the following, assume that p is true...Ch. 3 - In each of the following assume that p is true and...Ch. 3 - 15 Explain in your own words why, if p is a...Ch. 3 - State the necessary conditions for each of the...Ch. 3 - Construct a truth table for each of the following....Ch. 3 - Construct a truth table for each of the following....Ch. 3 - Decide whether each statement is true or false....Ch. 3 - Decide whether each statement is true or false.
20...Ch. 3 - Write each conditional statement in if... then...Ch. 3 - Write each conditional statement in if then form....Ch. 3 - Write each conditional statement in if… then...Ch. 3 - Write each conditional statement in if then form....Ch. 3 - For each statement in Exercises 25 and 26, write...Ch. 3 - Prob. 26TCh. 3 - Prob. 27TCh. 3 - 28 Match each argument in parts (a) - (d) in the...Ch. 3 - Use a truth table to determine whether each...Ch. 3 - Use a truth table to determine whether each...
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