Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 2.2, Problem 13E
To determine
To prove: The relation R is an equivalence relation on set S and describes the equivalence class containing the element
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In a company with 80 employees, 60 earn $10.00 per hour and 20 earn $13.00 per
hour.
Is this average hourly wage considered representative?
The following is a list of questions answered correctly on an exam. Calculate the
Measures of Central Tendency from the ungrouped data list.
NUMBER OF QUESTIONS ANSWERED CORRECTLY ON AN APTITUDE EXAM
112
72
69
97
107
73
92
76
86
73
126
128
118
127
124
82
104
132
134
83
92
108
96
100
92
115
76
91
102
81
95
141
81
80
106
84
119
113
98
75
68
98
115
106
95
100
85
94
106
119
The following ordered data list shows the data speeds for cell phones used by a
telephone company at an airport:
A. Calculate the Measures of Central Tendency using the table in point B.
B. Are there differences in the measurements obtained in A and C? Why (give at
least one justified reason)?
0.8
1.4
1.8
1.9
3.2
3.6
4.5
4.5
4.6
6.2
6.5
7.7
7.9
9.9
10.2
10.3
10.9
11.1
11.1
11.6
11.8
12.0
13.1
13.5
13.7
14.1
14.2
14.7
15.0
15.1
15.5
15.8
16.0
17.5
18.2
20.2
21.1
21.5
22.2
22.4
23.1
24.5
25.7
28.5
34.6
38.5
43.0
55.6
71.3
77.8
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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