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
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
R
2.3.32 2.5.3 4.4.16 8.3.9
3.1.3 E7.1.7 4.4.17 T8.3.3
U
3.1.4 7.1.7 5.1.14 6.2.8
3.1.6 E8.1.1 5.1.16 T6.2.9
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R
U
Analysis
SE
with an Introduction to Proof
IS
5th Edition
by Steven R. Lay
O
slay@leeuniversity.edu
N
Chapter 1 – Logic and Proof
N
Solutions to Exercises
O
Section 1.1 – Logical Connectives
C
1. (a) False: A statement may be false.
ED
(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.
M
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 ~ 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.
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