# A First Course in Abstract Algebra 3rd Edition Rotman Test Bank

~~$80.00~~ $12.99

# A First Course in Abstract Algebra 3^{rd} Edition Rotman Test Bank

ISBN-13: 978-0131862678

ISBN-10: 0131862677

# A First Course in Abstract Algebra 3^{rd} Edition Rotman Test Bank

ISBN-13: 978-0131862678

ISBN-10: 0131862677

# Be the best nurse you can be:

Nursing test banks are legit and very helpful. This test bank on this page can be downloaded immediately after you checkout today.

# Here is the definition of nursing

Its true that you will receive the entire legit test bank for this book and it can happen today regardless if its day or night. We have made the process automatic for you so that you don’t have to wait.

# We encourage you to purchase from only a trustworthy provider:

We take great care and love into helping our fellow nursing students during their advancement of their career. We also provide samples, if you want one just send us an email or check the bottom of this page to see if one is posted for you already.

# Have any comments or suggestions?

When you get your file today you will be able to open it on your device and start studying for your class right now.

# Free Nursing Test Questions:

1

Solution Manual for

A First Course in Abstract Algebra, with Applications

Third Edition

by Joseph J. Rotman

Exercises for Chapter 1

1.1 True or false with reasons.

(i) There is a largest integer in every nonempty set of negative integers.

Solution.

True. If C is a nonempty set of negative integers, then

−

C

={n

:

n

∈

C

}

is a nonempty set of positive integers. If

a

is the smallest element

of

C,

which exists by the Least Integer Axiom, then

a

≤c

for all c

∈

CRemember, that a

≥

c for all c

∈

C.

(ii) There is a sequence of 13 consecutive natural numbers containing

exactly 2 primes.

Solution. True. The integers 48 through 60 form such a sequence;

only 53 and 59 are primes.

(iii) There are at least two primes in any sequence of 7 consecutive

natural numbers.

Solution. False. The integers 48 through 54 are 7 consecutive

natural numbers, and only 53 is prime.

(iv) Of all the sequences of consecutive natural numbers not containing

2 primes, there is a sequence of shortest length.

Solution. True. The set C consisting of the lengths of such (ﬁnite)

sequences is a nonempty subset of the natural numbers.

(v) 79 is a prime.

Solution. True. √79 < √81

=

9, and 79 is not divisible by 2, 3,

5, or 7.

(vi) There exists a sequence of statements S(1), S(2),… with S(2n)

true for all n

≥

1 and with S(2n

1)

false for every n

≥

1.

Solution. True. Deﬁne S(2n

1)

to be the statement n

=

n, and

deﬁne S(2n) to be the statement n

=

n.

(vii) For all n

≥

0, we have n

≤

Fn , where Fn is the nth Fibonacci

number.