Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 2.1, Problem 40E
To determine
To prove: The set equality
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In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a
random sample of 1014 adults aged 18 and over. One of the questions was, "How many
cups of coffee, if any, do you drink on an average day?" The following table shows the
results obtained (Gallup website, August 6, 2012).
Number of Cups
per Day
0
1
2
3
4 or more
Number of
Responses
365
264
193
91
101
Define a random variable x = number of cups of coffee consumed on an average day. Let
x=4 represent four or more cups.
a. Develop a probability distribution for x.
b. Compute the expected value of x.
c. Compute the variance of x.
d. Suppose we are only interested in adults who drink at least one cup of coffee on an
average day. For this group, let y = the number of cups of coffee consumed on an
average day. Compute the expected value of y and compare it to the expected value of x.
Ten major college football bowl games were played in January 2010, with the University
of Alabama beating the University of Texas 37 to 21 to become the national champion
of college football. The results of the 10 bowl games follow (USA Today, January 8, 2010).
Bowl Game
Score
Outback
Gator
Auburn 38 Northwestern 35
Florida State 33 West Virginia 21
Capital One
Penn State 19 LSU 17
Rose
Ohio State 26 Oregon 17
Florida 51 Cincinnati 24
Sugar
Cotton
Alamo
Fiesta
Mississippi State 21 Oklahoma State 7
Texas Tech 41 Michigan State 31
Boise State 17 TCU 10
Orange
Iowa 24 Georgia Tech 14
Championship
Alabama 37 Texas 21
Predicted
Point Margin
Actual
Point Margin
5
3
1
12
3
-2
14
3
9
-4
-3
4
229740706
14
10
10
16
The predicted winning point margin was based on Las Vegas betting odds approximately
one week before the bowl games were played. For example, Auburn was predicted to beat
Northwestern in the Outback Bowl by five points. The actual winning point margin for Au-
burn was three points. A…
Chapter 2 Solutions
Discrete Mathematics
Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - In Exercises 5–8, compute A × B for each of the...Ch. 2.1 - In Exercises 5–8, compute A × B for each of the...Ch. 2.1 - In Exercises 5–8, compute A × B for each of the...Ch. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Give an example of sets for which , but A ≠ B.
Ch. 2.1 - Give an example of sets for which , but A ≠ B.
Ch. 2.1 - Give an example of sets for which , but A ≠ B.
Ch. 2.1 - Give an example of sets for which (A − B) − C ≠ A...Ch. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - If A is a set containing m elements and B is a set...Ch. 2.1 - Under what conditions is A − B = B − A?
Ch. 2.1 - Under what conditions is A ⋃ B = A?
Ch. 2.1 - Under what conditions is A ⋂ B = A?
Ch. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prove the set equalities in Exercises...Ch. 2.1 - Prob. 39ECh. 2.1 - Prove that (A × C) ⋃ (B × D) ⊆ (A ⋃ B) × (C ⋃ D).
Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1-12, determine which of the...Ch. 2.2 - Prob. 6ECh. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - Prob. 8ECh. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - Prob. 12ECh. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - Prob. 17ECh. 2.2 - In Exercises 13–18, show that the given relation R...Ch. 2.2 - Prob. 19ECh. 2.2 - Write the equivalence relation on {1, 2, 3, 4, 5,...Ch. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Let R1 and R2 be equivalence relations on sets S1...Ch. 2.2 - Determine the number of relations on a set S...Ch. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - How many partitions are there of a set containing...Ch. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 33ECh. 2.3 - In Exercises 1–8, determine whether the given...Ch. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Consider the “divides” relation on the set of...Ch. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Determine formulas for the functions gf and fg in...Ch. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - Prob. 49ECh. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - Prob. 52ECh. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - Find a subset Y of the set of real numbers X such...Ch. 2.4 - Find a subset Y of the set of real numbers X such...Ch. 2.4 - Prob. 63ECh. 2.4 - If X has m elements and Y has n elements, how many...Ch. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.4 - Prob. 69ECh. 2.4 - Prob. 70ECh. 2.5 - Compute the Fibonacci numbers F1 through F10.
Ch. 2.5 - Suppose that a number xn is defined recursively by...Ch. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - In Exercises 7–10, determine what is wrong with...Ch. 2.5 - In Exercises 11–26, prove each of the given...Ch. 2.5 - In Exercises 11–26, prove each of the given...Ch. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - In Exercises 11–26, prove each of the given...Ch. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - A sequence s0, s1, s2,… is called a geometric...Ch. 2.5 - A sequence, s0, s1, s2,… is called an arithmetic...Ch. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Evaluate the numbers in Exercises 1–12.
4. C(12,...Ch. 2.6 - Evaluate the numbers in Exercises 1–12.
5. C(11,...Ch. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Evaluate the numbers in Exercises 1–12.
8. C(13,...Ch. 2.6 - Evaluate the numbers in Exercises 1–12.
9. C(n,...Ch. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Evaluate the numbers in Exercises 1–12.
12.
Ch. 2.6 - Prob. 13ECh. 2.6 - How many nonempty subsets of the set {a, e, i, o,...Ch. 2.6 - At Avanti’s, a pizza can be ordered with any...Ch. 2.6 - If a test consists of 12 questions to be answered...Ch. 2.6 - Prob. 17ECh. 2.6 - Jennifer’s grandmother has told her that she can...Ch. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prove each of the statements in Exercises 29–40 by...Ch. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prove each of the statements in Exercises 29–40 by...Ch. 2.6 - Prob. 33ECh. 2.6 - Prove each of the statements in Exercises 29–40 by...Ch. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2 - Prob. 1SECh. 2 - Prob. 2SECh. 2 - Prob. 3SECh. 2 - Prob. 4SECh. 2 - Prob. 5SECh. 2 - Prob. 6SECh. 2 - Prob. 7SECh. 2 - Prob. 8SECh. 2 - Prob. 9SECh. 2 - Draw Venn diagrams depicting the sets in Exercises...Ch. 2 - Prob. 11SECh. 2 - Prob. 12SECh. 2 - Prob. 13SECh. 2 - Prob. 14SECh. 2 - Prob. 15SECh. 2 - Prob. 16SECh. 2 - Prob. 17SECh. 2 - Prob. 18SECh. 2 - Prob. 19SECh. 2 - Prob. 20SECh. 2 - Prob. 21SECh. 2 - Prob. 22SECh. 2 - Prob. 23SECh. 2 - Prob. 24SECh. 2 - Prob. 25SECh. 2 - Prob. 26SECh. 2 - Prob. 27SECh. 2 - Prob. 28SECh. 2 - Prob. 29SECh. 2 - Prob. 30SECh. 2 - Prob. 31SECh. 2 - Prob. 32SECh. 2 - Prob. 33SECh. 2 - Prob. 34SECh. 2 - Prob. 35SECh. 2 - How many equivalence relations on S = {a, b, c}...Ch. 2 - Prob. 37SECh. 2 - Prob. 38SECh. 2 - Prob. 39SECh. 2 - Prob. 40SECh. 2 - Prob. 41SECh. 2 - Prob. 42SECh. 2 - Prob. 43SECh. 2 - Prob. 44SECh. 2 - Prob. 45SECh. 2 - Prob. 46SECh. 2 - Prob. 47SECh. 2 - Prob. 49SECh. 2 - Prob. 50SECh. 2 - Prob. 51SECh. 2 - Prob. 52SECh. 2 - Prob. 53SECh. 2 - Prob. 54SECh. 2 - Prob. 55SECh. 2 - Prob. 56SECh. 2 - Prob. 57SECh. 2 - Prob. 58SECh. 2 - Prob. 59SECh. 2 - Prob. 60SECh. 2 - Prob. 61SECh. 2 - Prob. 62SECh. 2 - Prob. 63SECh. 2 - Prob. 64SECh. 2 - Prove the results in Exercises 63–72 by...Ch. 2 - Prob. 66SECh. 2 - Prob. 67SECh. 2 - Prob. 68SECh. 2 - Prob. 69SECh. 2 - Prob. 70SECh. 2 - Prob. 71SECh. 2 - Prob. 72SECh. 2 - Prob. 1CPCh. 2 - Prob. 6CPCh. 2 - Prob. 7CPCh. 2 - Prob. 12CP
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