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Table of contents
  1. Preface
  2. 1 Sets
    1. Introduction
    2. 1.1 Basic Set Concepts
    3. 1.2 Subsets
    4. 1.3 Understanding Venn Diagrams
    5. 1.4 Set Operations with Two Sets
    6. 1.5 Set Operations with Three Sets
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  3. 2 Logic
    1. Introduction
    2. 2.1 Statements and Quantifiers
    3. 2.2 Compound Statements
    4. 2.3 Constructing Truth Tables
    5. 2.4 Truth Tables for the Conditional and Biconditional
    6. 2.5 Equivalent Statements
    7. 2.6 De Morgan’s Laws
    8. 2.7 Logical Arguments
    9. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  4. 3 Real Number Systems and Number Theory
    1. Introduction
    2. 3.1 Prime and Composite Numbers
    3. 3.2 The Integers
    4. 3.3 Order of Operations
    5. 3.4 Rational Numbers
    6. 3.5 Irrational Numbers
    7. 3.6 Real Numbers
    8. 3.7 Clock Arithmetic
    9. 3.8 Exponents
    10. 3.9 Scientific Notation
    11. 3.10 Arithmetic Sequences
    12. 3.11 Geometric Sequences
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  5. 4 Number Representation and Calculation
    1. Introduction
    2. 4.1 Hindu-Arabic Positional System
    3. 4.2 Early Numeration Systems
    4. 4.3 Converting with Base Systems
    5. 4.4 Addition and Subtraction in Base Systems
    6. 4.5 Multiplication and Division in Base Systems
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  6. 5 Algebra
    1. Introduction
    2. 5.1 Algebraic Expressions
    3. 5.2 Linear Equations in One Variable with Applications
    4. 5.3 Linear Inequalities in One Variable with Applications
    5. 5.4 Ratios and Proportions
    6. 5.5 Graphing Linear Equations and Inequalities
    7. 5.6 Quadratic Equations with Two Variables with Applications
    8. 5.7 Functions
    9. 5.8 Graphing Functions
    10. 5.9 Systems of Linear Equations in Two Variables
    11. 5.10 Systems of Linear Inequalities in Two Variables
    12. 5.11 Linear Programming
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  7. 6 Money Management
    1. Introduction
    2. 6.1 Understanding Percent
    3. 6.2 Discounts, Markups, and Sales Tax
    4. 6.3 Simple Interest
    5. 6.4 Compound Interest
    6. 6.5 Making a Personal Budget
    7. 6.6 Methods of Savings
    8. 6.7 Investments
    9. 6.8 The Basics of Loans
    10. 6.9 Understanding Student Loans
    11. 6.10 Credit Cards
    12. 6.11 Buying or Leasing a Car
    13. 6.12 Renting and Homeownership
    14. 6.13 Income Tax
    15. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  8. 7 Probability
    1. Introduction
    2. 7.1 The Multiplication Rule for Counting
    3. 7.2 Permutations
    4. 7.3 Combinations
    5. 7.4 Tree Diagrams, Tables, and Outcomes
    6. 7.5 Basic Concepts of Probability
    7. 7.6 Probability with Permutations and Combinations
    8. 7.7 What Are the Odds?
    9. 7.8 The Addition Rule for Probability
    10. 7.9 Conditional Probability and the Multiplication Rule
    11. 7.10 The Binomial Distribution
    12. 7.11 Expected Value
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  9. 8 Statistics
    1. Introduction
    2. 8.1 Gathering and Organizing Data
    3. 8.2 Visualizing Data
    4. 8.3 Mean, Median and Mode
    5. 8.4 Range and Standard Deviation
    6. 8.5 Percentiles
    7. 8.6 The Normal Distribution
    8. 8.7 Applications of the Normal Distribution
    9. 8.8 Scatter Plots, Correlation, and Regression Lines
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  10. 9 Metric Measurement
    1. Introduction
    2. 9.1 The Metric System
    3. 9.2 Measuring Area
    4. 9.3 Measuring Volume
    5. 9.4 Measuring Weight
    6. 9.5 Measuring Temperature
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  11. 10 Geometry
    1. Introduction
    2. 10.1 Points, Lines, and Planes
    3. 10.2 Angles
    4. 10.3 Triangles
    5. 10.4 Polygons, Perimeter, and Circumference
    6. 10.5 Tessellations
    7. 10.6 Area
    8. 10.7 Volume and Surface Area
    9. 10.8 Right Triangle Trigonometry
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  12. 11 Voting and Apportionment
    1. Introduction
    2. 11.1 Voting Methods
    3. 11.2 Fairness in Voting Methods
    4. 11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem
    5. 11.4 Apportionment Methods
    6. 11.5 Fairness in Apportionment Methods
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  13. 12 Graph Theory
    1. Introduction
    2. 12.1 Graph Basics
    3. 12.2 Graph Structures
    4. 12.3 Comparing Graphs
    5. 12.4 Navigating Graphs
    6. 12.5 Euler Circuits
    7. 12.6 Euler Trails
    8. 12.7 Hamilton Cycles
    9. 12.8 Hamilton Paths
    10. 12.9 Traveling Salesperson Problem
    11. 12.10 Trees
    12. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  14. 13 Math and...
    1. Introduction
    2. 13.1 Math and Art
    3. 13.2 Math and the Environment
    4. 13.3 Math and Medicine
    5. 13.4 Math and Music
    6. 13.5 Math and Sports
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  15. A | Co-Req Appendix: Integer Powers of 10
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index

Chapter Test

For the following Exercises, use the figure shown.
Five graphs are titled graph S, graph T, graph U, graph V, and graph W. Graph S has five vertices: a, b, c, d, and e. Edges connect a b, a c, b c, c d, c e, and d e. Graph T has four vertices: a, b, d, and e. Edges connect a b, a e, b d, and d e. Graph U has 6 vertices: a, b, f, c, d, and e. Edges connect a b, a f, f d, b c, c d, d e, c e, and a c. Graph V has four vertices: a, b, d, and e.Edges connect a b, a d, a e, b d, and d e. Graph W has four vertices: a, b, d, and e. Edges connect a b, a d, and d e.
1.
Name the edges in Graph T.
2.
Identify the graph(s) with six edges.
For the following exercises, use the figure shown.
Four graphs are titled graph A, graph B, graph C, and graph D. Graph A shows edges connecting the vertices: v q, v p, v u, v t, v s and v r. Graph B shows edges connecting the vertices: p q, q s, s t, t p, v u, and v r. Graph C shows edges connecting the vertices: p q, p u, u t, u v, t s, q s, and p t. Graph D shows edges connecting the vertices: v p, v q, v u, v t, v r, v s, p q, u t, and r s.
3.
Identify any of the graphs that is a subgraph of Graph D.
4.
Identify any graphs with no cyclic subgraphs of any size.
5.
Consider Graph 4 and Graph 6 in the given figure. Determine if one graph is a subgraph of the other. If so, give a correspondence between vertices that demonstrates this relationship. If not, identify conflicting characteristics.
Four graphs. Graph 3 has two overlapping quadrilaterals. The vertices of the first quadrilateral are 1, 2, 3, and 4. The vertices of the second quadrilateral are 5, 6, 7, and 8. An edge connects 2 to 6. Graph 4 has two overlapping quadrilaterals. The vertices of the first quadrilateral are 9, 10, 13, and 14. The vertices of the second quadrilateral are 15, 11, 17, and 16. A vertex, 12 is at the intersection of 15 and 11 and 13 and 10. Graph 5 has two overlapping quadrilaterals. The vertices of the first quadrilateral are 18, 19, 20, and 21. The vertices of the second quadrilateral are 22, 23, 24, and 25. Graph 6 has two overlapping quadrilaterals. The vertices of the first quadrilateral are 28, 32, 33, and 34. The vertices of the second quadrilateral are 27, 29, 30, and 31 A vertex, 26 is at the intersection of 28 and 32 and 27 and 31.
6.
For the following exercise, use Graph A in the given figure. Consider each sequence of vertices. Determine if it is only a walk, both a walk and a path, both a walk and a trail, all three, or none of these.
Two graphs are labeled graph A and graph K. Graph A has five vertices: b, c, d, e, and f. Edges connect b c, c f, b d, b e, d e, and e f. Graph K has five vertices: m, n, o, p, and q. Edges connect m n, n o, n q, q o, o p, n p, and m p. debcf
7.
For the following exercise, use Graphs A and K in Figure 12.369. Determine the chromatic number of Graph K. Give a coloring that supports your conclusion.
For the following exercise, use the graphs and multigraphs in the given figure.
Five graphs. Graph 11 has 8 vertices. Edges connect r s, s v, v u u r, t x, t w, and x w. Graph 12 has 7 vertices. Edges connect ef, f g, g e, g d, e d, e a, d a, d c, g c, c a, c b, and a b. Graph 13 has 5 vertices. Edges connect n o, n q, o m, o p, m p, m q, and q p. Multigraph 14 has 5 vertices. The edges are labeled from A to H. Multigraph 15 has 5 vertices. The edges are labeled from K to U.
8.
Identify any graphs and/or multigraphs that are not Eulerian. If there are none, state so.
9.
List the set of vertices for each component in Graph 11.
10.
Find an Euler circuit beginning and ending at vertex b in Graph 12 if one exists.
11.
Use Fleury’s algorithm to construct an Euler trail for the given graph beginning at vertex f of your choice.
A graph has 7 vertices. The vertices are labeled a, b, c, d, e, f, and g. Edges connect ab, a d, d f, d e, f c, f g, c g, and e b.
12.
Use the graphs shown to determine whether the sequence of vertices dbcfed is a Hamilton cycle, an Euler circuit, both, or neither.
Two graphs are labeled graph A and graph K. Graph A has five vertices: b, c, d, e, and f. Edges connect b c, c f, b d, b e, d e, and e f. Graph K has five vertices: m, n, o, p, and q. Edges connect m n, n o, n q, q o, o p, n p, and m p.
13.
Calculate the number of distinct Hamilton cycles in a complete graph with 15 vertices.
14.
Use the figure shown to find the weight of the given Hamilton cycle:
twxuyvsrqt
Graph Z has nine vertices arranged in 3 rows and 3 columns. The vertices are as follows. Row 1: q, r, s. Row 2: t, u, v. Row 3; w, x, y. The edges are as follows. 1, q to t. 2, s to v. 3, r to s. 4, q to u. 5, u to y. 6, r to v. 7, r to u. 8, v to y. 9, w to x. 10, x to y. 1, u to x. 12, t to w. 13, q to r. 14, t to u. 15, u to v.
For the following exercises, use this information: For the Halloween celebration at an elementary school, the students from Classroom I will visit every classroom once and return to their own classroom. The floor plan of the school is given.
A floor plan of an elementary school. It has three blocks. The first block has front office A. The second block has three rooms: G, H, and I. The third block has five rooms: B, C, D, E, and F. Exit is at the top-right.
15.
Draw a graph to represent the classrooms of the elementary school in which each vertex is a classroom and an edge between two vertices indicates that there is a path between the two rooms that does not pass the door to another classroom.
16.
Use your graph to find a Hamilton circuit beginning and ending at I.
17.
Explain what the Hamilton circuit you found represents for the students in Classroom I.
18.
Find a Hamilton cycle of low weight for Graph 18, beginning at vertex q, and using the nearest neighborhood method. What is the weight of the cycle?
Two graphs are labeled graph 17 and graph 18. Graph 17 has four vertices, a, b, c, and d. The edges are labeled as follows: a to b, 13.3; b to c, 2.0; c to d, 8.7; d to a, 9.3; a to c, 1.5; b to d, 5.2. Graph 18 has five vertices, m, q, n, p, and o. The edges are labeled as follows: m to n, 250; m to q, 100; m to p, 110; m to 0, 300; q o n, 90; q to o, 210; n to p, 75; q to p, 50; p to o, 425; n to o, 225.
19.
Use Kruskal’s Algorithm to find a minimum spanning tree for the below graph. Graph the tree and give its weight.
A graph has five vertices. The vertices are A, C, D, G, and F. The edges are labeled as follows: C to A, 130; C to D, 35; C to G, 125; C to F, 20; A to D, 45; A to F, 70; D to G, 40; A to G, 100; G to F, 15; D to F, 30.
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