Skip to Main Content
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
Prove this statement by proving If i, then ii,”“If ii, then iii, and If iii, then i.
7. Let x and y be two distinct negative real numbers. The following statements are equivalent:
i. x < y,
ii. |x| > |y |, and
iii. x
2
> y
2
.
8. Consider the two systems of linear equations
S
1
:
a
1
x + b
1
y = c
1
a
2
x + b
2
y = c
2
(
and
S
2
:
a
1
x + b
1
y = c
1
ða
1
+ ba
2
Þx + ðb
1
+ bb
2
Þy = c
1
+ bc
2
(
with a
1
, a
2
, b
1
, b
2
, c
1
, c
2
real numbers and b 0. The pair of values (x
0
, y
0
) is a solution of S
1
if and
only if it is a solution of S
2
.
USE OF COUNTEREXAMPLES
An example can be very useful when trying to make a point or explain the result obtained in a proof, b ut it
cannot be used as a proof of ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Discrete Structures, Logic, and Computability, 4th Edition

Discrete Structures, Logic, and Computability, 4th Edition

James L. Hein

Publisher Resources

ISBN: 9780123822178