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Contemporary Mathematics

Chapter Review

Contemporary MathematicsChapter Review
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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 Review

Basic Set Concepts
1.
A ______________ is a well-defined collection of distinct objects.
2.
A collection of well-defined objects without any members in it is called the ________ _______.
3.
Write the set consisting of the last five letters of the English alphabet using the roster method.
4.
Write the set consisting of the numbers 1 through 20 inclusive using the roster method and an ellipsis.
5.
Write the set of all zebras that do not have stripes in symbolic form.
6.
Write the set of negative integers using the roster method and an ellipsis.
7.
Use set builder notation to write the set of all even integers.
8.
Write the set of all letters in the word Mississippi and label it with a capital M.
9.
Determine whether the following collection describes a well-defined set: "A group of these five types of apples: Granny Smith, Red Delicious, McIntosh, Fuji, and Jazz."
10.
Determine whether the following collection describes a well-defined set: "A group of five large dogs."
11.
Determine the cardinality of the set A = \{ {\text{Alabama}},{\text{ Alaska}},{\text{ Arkansas}},{\text{ Arizona}}\}.
12.
Determine whether the following set is a finite set or an infinite set: F = \{ 5,10,15, \ldots \}.
13.
Determine whether sets A and B are equal, equivalent, or neither: A = \{a,b,c\} and B = \{ 1,2,3,4\}.
14.
Determine if sets A and B are equal, equivalent, or neither: A = \{a, b,c\} and B = \{c,a,b\}.
15.
Determine if sets A and B are equal, equivalent, or neither: A = \{a,b,c\} and B = \{ 1,2,3\}.
Subsets
16.
If every member of set A is also a member of set B, then set A is a _________ of set B.
17.
Determine whether set A is a subset, proper subset, or neither a subset nor proper subset of set B: A = \{s,o,n\} and B = \{s,o,n,g\}.
18.
Determine whether set A is a subset, proper subset, or neither a subset nor proper subset of set B: A = \{s,o,n\} and B = \{s,o,l\}.
19.
Determine whether set A is a subset, proper subset, or neither a subset nor proper subset of set B: A = \{s,o,n\} and B = \{o,n,s\}.
20.
List all the subsets of the set \{ {\text{up,}}\,{\text{down}}\}.
21.
List all the subsets of the set \{ 0\}.
22.
Calculate the total number of subsets of the set {Scooby, Velma, Daphne, Shaggy, Fred}.
23.
Calculate the total number of subsets of the set {top hat, thimble, iron, shoe, battleship, cannon}.
24.
Find a subset of the set \{g,r,e,a,t\} that is equivalent, but not equal, to \{t,e,a\}.
25.
Find a subset of the set \{g,r,e,a,t\} that is equal to \{t,e,a\}.
26.
Find two equivalent finite subsets of the set of natural numbers, \mathbb{N} = \{ 1,2,3, \ldots \}, with a cardinality of 4.
27.
Find two equal finite subsets of the set of natural numbers, \mathbb{N} = \{ 1,2,3, \ldots \}, with a cardinality of 3.
Understanding Venn Diagrams
28.
Use the Venn diagram below to describe the relationship between the sets, symbolically and in words:
A one-set Venn diagram is labeled E equals Elms. The union of the Venn diagram is marked U equals Trees.
29.
Use the Venn diagram below to describe the relationship between the sets, symbolically and in words:
A two-set Venn diagram not intersecting one another is given. The first set is labeled Planes while the second set is labeled Trains. The union of the Venn diagram is marked U equals Modes of Transportation.
30.
Draw a Venn diagram to represent the relationship between the described sets: Falcons \subset Raptors.
31.
Draw a Venn diagram to represent the relationship between the described sets: Natural numbers \subset Integers \subset Real numbers.
32.
The universal set is the set U = \{s,m,i,l,e\}. Find the complement of the set E = \{e,l,m\}.
33.
The universal set is the set U = \{ 1,2,3, \ldots \}. Find the complement of the set V = \{ 18,19,20, \ldots \}.
34.
Use the Venn diagram below to determine the members of the set {A^\prime }.
A one-set Venn diagram of A shows (d, e, a, r). The union of the Venn diagram is marked U equals (r, e, a, d, i, n, g).
35.
Use the Venn diagram below to determine the members of the set {A^\prime }.
A one-set Venn diagram of A shows (g, r, a, n, d). The union of the Venn diagram is marked U equals (r, e, a, d, i, n, g).
Set Operations with Two Sets
Determine the union and intersection of the sets indicated: U = \{ a,b,c, \ldots ,z\}, S = \{s,c,r,a,b,l,e\}, B = \{b,r,a,c,e\}, C = \{c,r,a,b\}, R = \{r,i,s,k\}, and Q = \{q,u,i,z\}.
36.
What is S \cap R?
37.
What is S \cup B?
38.
Write the set containing the elements in sets B\,{\text{or}}\,Q.
39.
Write the set containing all the elements is both sets B\,{\text{and}}\,Q.
40.
Find C\,{\text{intersection}}\,R.
41.
Find C\,{\text{union}}\,R.
42.
Find the cardinality of C \cup R,\,n(C \cup R).
43.
Find n(S\,{\text{union}}\,R).
44.
Use the Venn diagram below to find A \cap B.
A two-set Venn diagram of A and B intersecting one another is given. Set A shows d, r while set B shows f. The intersection of the sets shows a, k, e. The union of the Venn diagrams is marked (a, b, c, …, z).
45.
Use the Venn diagram below to find n(A \cup B).
A two-set Venn diagram of A and B intersecting one another is given. Set A shows 5 while set B shows 2. The intersection of the sets shows 7. Outside the intersection of Venn diagrams, 10 is marked. The union of the Venn diagram is 24.
Set Operations with Three Sets
Use the Venn diagram below to answer the following questions.
A three-set Venn diagram of A, B, and C overlapping one another is given. Set A shows 7, set B shows 3 and set C shows 12. Overlapping of sets A and B shows 4, overlapping of sets B and C shows 8, and overlapping of A and C plus shows 5. Overlapping of A, B, and C shows 2. Outside the intersection of Venn diagrams, 6 is marked. The union of the Venn diagram is 47.
46.
Find n(A \cup C).
47.
Find n(B \cap C).
48.
A food truck owner surveyed a group of 50 customers about their preferences for hamburger condiments. After tallying the responses, the owner found that 24 customers preferred ketchup, 11 preferred mayonnaise, and 31 preferred mustard. Of these customers, eight preferred ketchup and mayonnaise, one preferred mayonnaise and mustard, and 13 preferred ketchup and mustard. No customer preferred all three. The remaining customers did not select any of these three condiments. Draw a Venn diagram to represent this data.
49.
Given U = \{ {\text{r,}}\,{\text{s,}}\,{\text{t,}}\,{\text{l,}}\,{\text{n,}}\,{\text{e,}}\,{\text{i,}}\,{\text{a}}\}, R = \{ {\text{r,}}\,{\text{e,}}\,{\text{s,}}\,{\text{t}}\}, S = \{ {\text{s,}}\,{\text{t,}}\,{\text{a,}}\,{\text{i,}}\,{\text{r}}\}, and L = \{ {\text{l,}}\,{\text{i,}}\,{\text{n,}}\,{\text{e,}}\,{\text{s}}\}, find (S \cup R) \cap {L^\prime }.
50.
Use Venn diagrams to prove that if A \subset B, then {B^\prime } \subset {A^\prime }.
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