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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
CHAPTER
3
Special Kinds of Theorems
There are several kinds of theorems whose proofs follow rather standard structures. In this chapter we
will look at some of the most important and common of these special theorems.
IF AND ONLY IF OR EQUIVALENCE THEOREMS
Statements including the expression if and only if are rather common and very useful in mathematics. If
we can show that A if and only if B, we are proving that A and B are (logically) equiva lent statements,
because either one of them i s true (or false) only when the other one is true (or false). The statement
A ifandonlyifB means that A is a necessary and sufficient condition for B
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Publisher Resources

ISBN: 9780123822178