SOLUTIONS MANUAL — Analysis with an Introduction to Proof, 5th Edition — Steven R. Lay — ISBN 9780137546138

INSTRUCTOR’S
SOLUTIONS MANUAL

A NALYSIS WITH AN




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I NTRODUCTION TO PROOF




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FIFTH EDITION



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Steven Lay
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Boston Columbus Indianapolis New York San Francisco Upper Saddle River
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Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo

, Instructor’s Solutions Manual
to accompany




ANALYSIS




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with an Introduction
to Proof




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5th Edition


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Steven R. Lay
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Upper Saddle River, New Jersey 07458




Copyright © 2014 Pearson Education, Inc.

, 3


Table of Starred Exercises
Note: The prefix P indicates a practice problem, the prefix E indicates an example, the prefix T refers to a
theorem or corollary, and the absence of a prefix before a number indicates an exercise.

Starred Starred
Exercise Later Use Exercise Later use
2.1.26 T3.4.11 4.3.14 4.4.5
2.2.10 2.4.26 4.4.10 8.2.14




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2.3.32 2.5.3 4.4.16 8.3.9
3.1.3 E7.1.7 4.4.17 T8.3.3




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3.1.4 7.1.7 5.1.14 6.2.8
3.1.6 E8.1.1 5.1.16 T6.2.9




SE
3.1.7 4.3.10, 4.3.15, E8.1.7, T9.2.9 5.1.18 5.2.14, 5.3.15
3.1.8 P8.1.3 5.1.19 5.2.17
3.1.24 4.1.7f, E5.3.7 5.2.10 T7.2.8
3.1.27 3.3.14 5.2.11 7.2.9b
3.1.30b
3.2.6a
3.3.11, E4.1.11, 4.3.14
4.1.9a, T4.2.1, 6.2.23, 7.2.16, T9.2.9 IS
5.2.13
5.2.16
T5.3.5, T6.1.7, 7.1.13
9.2.15
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3.2.6b T6.3.8 5.3.13b T6.2.8, T6.2.10
3.2.6c T4.1.14 6.1.6 6. 2.14, 6.2.19
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3.2.7 T8.2.5 6.1.8 7.3.13
3.3.7 T7.2.4, 7.2.3 6.1.17b 6.4.9
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3.3.12 7.1.14, T7.2.4 6.2.8 T7.2.1
3.4.15 3.5.12, T4.3.12 6.3.13d 9.3.16
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3.4.21 3.5.7 7.1.12 P7.2.5
3.5.8 9.2.15 7.1.13 7.2.5
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3.6.12 5.5.9 7.1.16 7.2.17
4.1.6b E4.2.2 7.2.9a P7.3.7
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4.1.7f T4.2.7, 4.3.10, E8.1.7 7.2.11 T8.2.13
4.1.9a 5.2.10, 9.2.17 7.2.15 7.3.20
4.1.11 E4.3.4 7.2.20 E7.3.9
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4.1.12 5.1.15 8.1.7 E8.2.6
4.1.13 5.1.13 8.1.8 8.2.13
4.1.15b 4.4.11, 4.4.18, 5.3.12 8.1.13a 9.3.8
4.1.16 5.1.15 8.2.12 9.2.7, 9.2.8
4.2.17 E6.4.3 8.2.14 T8.3.4
4.2.18 5.1.14, T9.1.10 9.1.15a 9.2.9




Copyright © 2014 Pearson Education, Inc.

, Section 1.1 x Logical Connectives 4


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R
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Analysis

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with an Introduction to Proof

IS
5th Edition

by Steven R. Lay
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N

Chapter 1 – Logic and Proof
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Solutions to Exercises
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Section 1.1 – Logical Connectives
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1. (a) False: A statement may be false.
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(b) False: A statement cannot be both true and false.
(c) True: See the comment after Practice 1.1.4.
(d) False: See the comment before Example 1.1.3.
(e) False: If the statement is false, then its negation is true.
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2. (a) False: p is the antecedent.
(b) True: Practice 1.1.6(a).
(c) False: See the paragraph before Practice 1.1.5.
(d) False: “p whenever q” is “if q, then p”.
(e) False: The negation of p º q is p š ~ q.

3. Answers in Book: (a) The 3 × 3 identity matrix is not singular.
(b) The function f (x) = sin x is not bounded on .
(c) The function f is not linear or the function g is not linear.
(d) Six is not prime and seven is not odd.
(e) x is in D and f (x) t 5.




Copyright © 2014 Pearson Education, Inc.