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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
Exercises
1. Explain why addition and subtraction are not binary operations on
= f0g= fall rational nonzero numbersg:
2. On the set M
2
= A =
a
11
a
12
a
21
a
22

with a
ij
real numbers

,letA and B be two elem ents of M
2
,then
define the operation
A B =
a
11
a
12
a
21
a
22

b
11
b
12
b
21
b
22

=
a
11
b
11
a
12
b
12
a
21
b
21
a
22
b
22

:
Is this a binary operation on M
2
? Explain.
3. On the set = ff : ℝ→ℝjf is a function defined for all real numbersg define the product operation. If
f and g are two elements of , their product is the function fg defined as
fgðxÞ= f ðxÞgðxÞ:
Is this a binary operation on ? Explain.
Define the quotient function
f
g
as
f
g
ðxÞ=
f ðxÞ
gð x Þ
:
Is this a binary
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Publisher Resources

ISBN: 9780123822178