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SOLUTIONS TO SELECTED
EXERCISES IN

THE
LOGIC
BOOK
Fourth Edition

MERRIE BERGMANN Smith College
JAMES MOOR Dartmouth College
JACK NELSON University of Washington, Tacoma

Boston Burr Ridge, IL Dubuque, IA Madison, WI New York
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Solutions to Selected Exercises in
THE LOGIC BOOK
Merrie Bergmann
James Moor
Jack Nelson
Published by McGraw-Hill, an imprint of The McGraw-Hill Companies, Inc., 1221
Avenue of the Americas, New York, NY 10020. Copyright © 2004, 1998, 1990, 1980
by The McGraw-Hill Companies, Inc. All rights reserved.
No part of this publication may be reproduced or distributed in any form or byany means, or stored in a database or retrieval system, without the prior written
consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any
network or other electronic storage or transmission, or broadcast for distance learning.
1 2 3 4 5 6 7 8 9 0 EVA/EVA 0 9 8 7 6 5 4 3
ISBN 0-07-248699-6
Vice president and Editor-in-chief: Thalia Dorwick
Publisher: ChristopherFreitag
Sponsoring editor: Jon-David Hague
Editorial assistant: Allison Rona
Marketing manager: Zina Craft
Project manager: Jen Mills
Associate supplement producer: Mel Valentín
Production supervisor: Tandra Jorgensen
Compositor: The GTS Companies/York, PA Campus
Typeface: 10/12 New Baskerville
CD Duplication: Eva-Tone

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CONTENTS

SOLUTIONS TO CHAPTER 1

1

SOLUTIONSTO CHAPTER 2

10

SOLUTIONS TO CHAPTER 3

20

SOLUTIONS TO CHAPTER 4

40

SOLUTIONS TO CHAPTER 5

88

SOLUTIONS TO CHAPTER 6

134

SOLUTIONS TO CHAPTER 7

148

SOLUTIONS TO CHAPTER 8

162

SOLUTIONS TO CHAPTER 9

198

SOLUTIONS TO CHAPTER 10

262

SOLUTIONS TO CHAPTER 11

304
Contents iii

SOLUTIONS TO SELECTED EXERCISES

CHAPTER ONE
Section 1.3E1.a. This sentence does have a truth-value and does fall within the scope
of this text. It is false if by ‘second President of the United States’ we mean
the second person to hold the office of President as established by the Constitution of the United States. However, it is true if we mean the second person to bear the title ‘President of the United States’, as the Articles of Confederation, whichpredate the Constitution, established a loose union of states
whose first and only president, John Hanson, did bear the title ‘President of
the United States.
c. This is a request or command, as such it is neither true nor false,
and therefore does not fall within the scope of this text.
e. This sentence does have a truth-value (it is true), and does fall
within the scope of this text.
g.This sentence does have a truth-value and does fall within the scope
of this text. It is false, as Bill Clinton is the President who immediately preceded George W. Bush.
i. This sentence is neither true nor false, for if it were true, then sentence m would be true, and if m is true then what it says, that m is false, is
also true. And no sentence can be both true and false. See the answer toexercise m below.
SOLUTIONS TO SELECTED EXERCISES ON PP. 10–12

1

k. This sentence gives advice and is neither true nor false. Hence it
does not fall within the scope of this text.
m. This appears to be a straightforward, unproblematic claim. But it is
not. In fact, it embodies a well-known paradox. For if what the sentence says is
true, then the sentence itself is, as is claimed, false.And if what the sentence says
is false, then the sentence is not false and therefore is true. So the sentence is
true if and only if it is false, an impossibility. This is an example of the paradox
of self-reference. We exclude paradoxical sentences from the scope of this text.
2.a. When Mike, Sharon, Sandy, and Vicky are all out of the office no
important decisions get made.
Mike is off...
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