The Heart of Mathematics: An Invitation to Effective Thinking
4th Edition
ISBN: 9781118156599
Author: Edward B. Burger, Michael Starbird
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 3.2, Problem 23MS
Prune growth. Is it possible to remove things from a set so that the collection of remaining things is larger than the original set? Explain why or why not. Illustrate with an example.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Find a second-order homogeneous linear ODE for which 1, e3x are solutions
Section 2.2 Subsets
71
Exercise Set 2.2
Practice Exercises
In Exercises 1-18, write or in each blank so that the resulting
statement is true.
1. {1, 2, 5}
{1, 2, 3, 4, 5, 6, 7}
2. {2, 3, 7}
{1, 2, 3, 4, 5, 6, 7}
3. {-3, 0, 3}
{-4,-3,-1, 1, 3, 4}
4. {-4, 0, 4}
5. {Monday, Friday}
{-3, -1, 1, 3}
{Saturday, Sunday, Monday, Tuesday, Wednesday}
6. {Mercury, Venus, Earth}
{Venus, Earth, Mars, Jupiter}
7. {x/x is a cat}
{xx is a black cat}
{x|x is a pure-bred dog}
ibrary
mbers,
ause the
entire
sual
8. {xx is a dog}
9. (c, o, n, v, e, r, s, a, t, i, o, n}
{v, o, i, c, e, s, r, a, n, t, o, n}
10. [r, e, v, o, l, u, t, i, o, n}
{t, o, l, o, v, e, r, u, i, n}
33. A = {x|x E N
and
5 < x < 12}
B
=
{x|x E N
and
2 ≤ x ≤ 11}
A_ B
34. A =
{x|x = N
and
3 < x < 10}
B =
A.
{x|x = N
and
2 ≤ x ≤ 8}
B
35. Ø
{7, 8, 9,..., 100}
36. Ø
_{101, 102, 103, . . ., 200}
37. [7, 8, 9,...}
38. [101, 102, 103, ...}
39. Ø
40. { }
{ }
e
In Exercises 41-54, determine whether each statement is true or
false. If…
A truck loaded with rocks weighs 14,260 lb. If the truck weighs 8420 lb, how much do the rocks weigh?
Chapter 3 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Ch. 3.1 - Still the one. What is a one-to-one...Ch. 3.1 - Prob. 2MSCh. 3.1 - Numerical nephwe. At a family gathering, your...Ch. 3.1 - Pile of packs. You walk into class late and notice...Ch. 3.1 - Bunch of balls. Your first job every morning at...Ch. 3.1 - The same, but unsure how much (H). We have used a...Ch. 3.1 - Taking stock (S). It turns out that there is a...Ch. 3.1 - Prob. 8MSCh. 3.1 - Heres looking @ ®. The following collections...Ch. 3.1 - Enough underwear. When Deb packs for a trip, she...
Ch. 3.1 - 791ZWV. Suppose a stranger tells you that the...Ch. 3.1 - 2452345. Suppose a stranger tells you that her...Ch. 3.1 - Social security (H). Is there a one-to-one...Ch. 3.1 - Testing one two three. A professor wishes to...Ch. 3.1 - Laundry day (ExH). Suppose you are given a bag of...Ch. 3.1 - Hair counts. Do there exist two nonbald people on...Ch. 3.1 - Social number (S). Social Security numbers contain...Ch. 3.1 - Prob. 18MSCh. 3.1 - Dining hall blues. One day in Ralph P. Uke Dining...Ch. 3.1 - Dorm life(H). Every student at a certain college...Ch. 3.1 - Pigeonhole principle. Recall the Pigeonhole...Ch. 3.1 - Mother and child. Every child has one and only one...Ch. 3.1 - Coast to coast. Jessica is working part-time from...Ch. 3.1 - An interesting correspondence. Suppose you invest...Ch. 3.1 - Chicken Little. With increased attention to eating...Ch. 3.1 - Table for four. The table below shows a one-to-one...Ch. 3.1 - Square table. The table below shows a one-to-one...Ch. 3.2 - Au natural. Describe the set of natural numbers.Ch. 3.2 - Prob. 2MSCh. 3.2 - Set setup. We can denote the natural numbers...Ch. 3.2 - Little or large. Which of the sets in Mindscape 3...Ch. 3.2 - A word you can count on. Define the cardinality of...Ch. 3.2 - Prob. 6MSCh. 3.2 - Naturally even. Let E stand for the set of all...Ch. 3.2 - Fives take over. Let EIF be the set of all natural...Ch. 3.2 - Six times as much (EH). If we let N stand for the...Ch. 3.2 - Any times as much. If we let N stand for the set...Ch. 3.2 - Missing 3 (H). Let TIM be the set of all natural...Ch. 3.2 - One weird set. Let OWS (you figure it out) be the...Ch. 3.2 - Squaring off. Let S stand for the set of all...Ch. 3.2 - Counting Cubes (formerly Crows). Let C stand for...Ch. 3.2 - Reciprocals. Suppose R is the set defined by R={...Ch. 3.2 - Hotel Cardinality (formerly California) (H). It is...Ch. 3.2 - Hotel Cardinality continued. Given the scenario in...Ch. 3.2 - More Hotel C (EH). Given the scenario in Mindscape...Ch. 3.2 - So much sand. Prove that there cannot be an...Ch. 3.2 - Prob. 20MSCh. 3.2 - Pruning sets. Suppose you have a set. If you...Ch. 3.2 - A natural prune. Describe a collection of numbers...Ch. 3.2 - Prune growth. Is it possible to remove things from...Ch. 3.2 - Same cardinality? Suppose we have two sets and we...Ch. 3.2 - Still the same? (S). Suppose we have two sets, and...Ch. 3.2 - Modest rationals (H). Devise and then describe a...Ch. 3.2 - A window of rationals. Using your answer to...Ch. 3.2 - Bowling ball barrel. Suppose you have infinitely...Ch. 3.2 - Not a total loss. Take the set of natural numbers...Ch. 3.2 - Prob. 30MSCh. 3.2 - Piles of peanuts (ExH). You have infinitely many...Ch. 3.2 - The big city (S). Not-Finite City (also known as...Ch. 3.2 - Dont lose your marbles. Suppose you have...Ch. 3.2 - Make a guess. Guess an infinite set that does not...Ch. 3.2 - Coloring. Consider the infinite collection of...Ch. 3.2 - Ping-Pong balls on parade (H). This Mindscape is...Ch. 3.2 - Primes. Show that the set of all prime numbers has...Ch. 3.2 - A grand union. Suppose you have two sets, and each...Ch. 3.2 - Unnoticeable pruning. Suppose you have any...Ch. 3.2 - Pink ping pong possibilities. You have a box...Ch. 3.2 - Plot the dots (H). The table below gives a...Ch. 3.2 - 1 to 1 or not 1 to 1? Does the table below give a...Ch. 3.2 - Roommates. Your school has 4000 students who want...Ch. 3.3 - Shake em up. What did Georg Cantor do that shook...Ch. 3.3 - Detecting digits. Heres a list of three numbers...Ch. 3.3 - Delving into digits. Consider the real number...Ch. 3.3 - Undercover friend (ExH). Your friend gives you a...Ch. 3.3 - Underhanded friend. Now you friend shows, you a...Ch. 3.3 - Dodgeball. Revisit the game of Dodgeball from...Ch. 3.3 - Dont dodge the connection (S). Explain the...Ch. 3.3 - Cantor with 3s and 7s. Rework Cantors proof from...Ch. 3.3 - Cantor with 4s and 8s. Rework Cantors proof from...Ch. 3.3 - Think positive. Prove that the cardinality of the...Ch. 3.3 - Diagonalization. Cantors proof is often referred...Ch. 3.3 - Digging through diagonals. First, consider the...Ch. 3.3 - Coloring revisited (ExH). In Mindscape 35 of the...Ch. 3.3 - Prob. 14MSCh. 3.3 - The first digit (H). Suppose that, in constructing...Ch. 3.3 - Ones and twos (H). Show that the set of all real...Ch. 3.3 - Pairs (S). In Cantors argument, is it possible to...Ch. 3.3 - Three missing. Given a list of real numbers, as in...Ch. 3.3 - Prob. 19MSCh. 3.3 - Prob. 20MSCh. 3.3 - Nines. Would Cantors argument work if we used 2...Ch. 3.3 - Missing irrational. Could you modify the...Ch. 3.3 - Logging cardinality. The function graphed here is...Ch. 3.3 - U-graph it. Using a graphic or on-line calculator,...Ch. 3.3 - Is a square a one-to-one correspondence? (H)...Ch. 3.3 - Is a cube a one-to-one correspondence? Sketch a...Ch. 3.3 - Find the digit. Your friend is thinking of a real...Ch. 3.4 - Prob. 1MSCh. 3.4 - Power play. Define the power set of a given set.Ch. 3.4 - Prob. 3MSCh. 3.4 - Prob. 4MSCh. 3.4 - Solar power. What is the cardinality of the power...Ch. 3.4 - All in the family (ExH). A family of four tries to...Ch. 3.4 - Making an agenda (H). There are eight members on...Ch. 3.4 - The power of sets (S). Let S={ !,@,#,$,%, }. Below...Ch. 3.4 - Prob. 9MSCh. 3.4 - Identifying the power. Let S be the set given by...Ch. 3.4 - Prob. 11MSCh. 3.4 - Another two. Suppose S is the set defined by S={...Ch. 3.4 - Prob. 13MSCh. 3.4 - Finite Cantor (H). Suppose that S is the set...Ch. 3.4 - One real big set. Describe (in words) a set whose...Ch. 3.4 - Prob. 16MSCh. 3.4 - The Ultra Grand Hotel (S). Could there be an...Ch. 3.4 - Prob. 18MSCh. 3.4 - Prob. 19MSCh. 3.4 - The number name paradox. Let S be the set of all...Ch. 3.4 - Adding another. Suppose that you have any infinite...Ch. 3.4 - Ones and twos. Describe a one-to-one...Ch. 3.4 - Enjoying the exponential function. Consider the...Ch. 3.4 - Prob. 28MSCh. 3.4 - Power play. Simplify the following expressions:...Ch. 3.4 - Powerful products. For each funciton given below,...Ch. 3.4 - Generalizing equality. Throughout this chapter we...Ch. 3.5 - Lining up. Can you draw a line segment that has...Ch. 3.5 - Reading between the lines. Use the figure below to...Ch. 3.5 - De line and Descartes. Put line segments L and M...Ch. 3.5 - Red line rendezvous (H). Given the equation for...Ch. 3.5 - Rendezvous two. Given the equation for the red...Ch. 3.5 - A circle is a cirde (H). Prove that a small circle...Ch. 3.5 - A circle is a square. Prove that a small circle...Ch. 3.5 - A circle is a triangle. Prove that a small circle...Ch. 3.5 - Stereo connections (ExH). Given the stereogiaphic...Ch. 3.5 - More stereo connections. Given the stereographic...Ch. 3.5 - Perfect shuffle problems (H). Suppose we used our...Ch. 3.5 - More perfect shuffle problems. Suppose we used our...Ch. 3.5 - Gouping digits. Given the grouping of digits...Ch. 3.5 - Where it came from. Given the grouping of digits...Ch. 3.5 - Group fix (S). Consider the point on the line from...Ch. 3.5 - Is there more to a cube? Prove that the...Ch. 3.5 - T and L (H). Prove that the cardinalities of...Ch. 3.5 - Infinitely long is long. Must it be the case that...Ch. 3.5 - Plugging up the north pole (ExH). What would...Ch. 3.5 - 3D stereo (S). Let S be the set of points on the...Ch. 3.5 - Stereo images. Given your answer to the preceding...Ch. 3.5 - Ground shuffle. Carefully verify that the pairing...Ch. 3.5 - Giving the rolled-up interval a tan. The graph...Ch. 3.5 - Back and forth. The function y=5x2 gives a...Ch. 3.5 - Forth and back. The function y=3x+1 gives a...Ch. 3.5 - Lining up (H). Find a function that gives a...Ch. 3.5 - Queuing up. Find a function that gives a...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Length of a Guy Wire A communications tower is located at the top of a steep hill, as shown. The angle of incli...
Precalculus: Mathematics for Calculus (Standalone Book)
Assessment 1-1A How many triangles are in the following figure?
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Constructing and Graphing Discrete Probability Distributions In Exercises 19 and 20, (a) construct a probabilit...
Elementary Statistics: Picturing the World (7th Edition)
Find how many SDs above the mean price would be predicted to cost.
Intro Stats, Books a la Carte Edition (5th Edition)
Fill in each blank so that the resulting statement is true. If n is a counting number, bn, read ______, indicat...
College Algebra (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Find the lengths of r, s, t, and u shown in the figure below if r+s=34. Round your answers to the nearest tenth. Note that the figure is not drawn to scale. 16 37° r = S u = t S u 24 ☑arrow_forwardFind the lengths of w, x, y, and z shown in the figure below if xy=69. Round your answers to the nearest tenth. Note that the figure is not drawn to scale. w= x= z= 16 37° W 24 Х Zarrow_forwardIn each of Problems 1 through 4, draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t → ∞. If this behavior depends on the initial value of y at t = 0, describe the dependency.1. y′ = 3 − 2yarrow_forward
- A = 5.8271 ± 0.1497 = B 1.77872 ± 0.01133 C=0.57729 ± 0.00908 1. Find the relative uncertainty of A, B, and C 2. Find A-3 3. Find 7B 4. Find A + B 5. Find A B-B - 6. Find A * B 7. Find C/B 8. Find 3/A 9. Find A 0.3B - 10. Find C/T 11. Find 1/√A 12. Find AB²arrow_forwardPlease help on question 16b attached. thxarrow_forwardMath 60arrow_forward
- math 62arrow_forwardB 2- The figure gives four points and some corresponding rays in the xy-plane. Which of the following is true? A B Angle COB is in standard position with initial ray OB and terminal ray OC. Angle COB is in standard position with initial ray OC and terminal ray OB. C Angle DOB is in standard position with initial ray OB and terminal ray OD. D Angle DOB is in standard position with initial ray OD and terminal ray OB.arrow_forwardtemperature in degrees Fahrenheit, n hours since midnight. 5. The temperature was recorded at several times during the day. Function T gives the Here is a graph for this function. To 29uis a. Describe the overall trend of temperature throughout the day. temperature (Fahrenheit) 40 50 50 60 60 70 5 10 15 20 25 time of day b. Based on the graph, did the temperature change more quickly between 10:00 a.m. and noon, or between 8:00 p.m. and 10:00 p.m.? Explain how you know. (From Unit 4, Lesson 7.) 6. Explain why this graph does not represent a function. (From Unit 4, Lesson 8.)arrow_forward
- Make up two polynomial functions, f(x) and g(x). • f(x) should be of degree 3 or higher. g(x) should be of degree 4 or higher. • Find f(3) in each of the three ways: substitution, remainder theorem (synthetic division), and long division. You should get the same answer three times for f(3). Find g(-2) once using your choice of the three methods.arrow_forwardere are many real-world situations that exhibit exponential and logarithmic nctions. • Describe two real world scenarios, one exponential and one logarithmic. Do not identify yet whether your scenarios are logarithmic or exponential.arrow_forwardLauris Online Back to Subject 不 4 ப 12 2 points T 35° 25° R M 4 N P 6Q 5 What is m/MNT? 120 T 12 What is the length of MR? 120 units 167:02:04 Time Remaining Yama is designing a company logo. The company president requested for the logo to be made of triangles. Yama is proposing the design shown. C 64°F Clear Q Search L 13 Ide dia des You scre Edi 12 L Tarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Quadrilaterals: Missing Angles and Sides; Author: rhornfeck;https://www.youtube.com/watch?v=knVj1O0L2TM;License: Standard YouTube License, CC-BY
STD IX | State Board | Types of Quadrilateral; Author: Robomate;https://www.youtube.com/watch?v=wh0KQ4UB0EU;License: Standard YouTube License, CC-BY