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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
Thus
b = bðsa + pt Þ
= ðkpÞs + bpt
= pðks + btÞ:
This implies that p divides b (explain why).
PROOF BY CONTRAPOSITIVE
In some cases we canno t use the kind of direct, straightforward arguments we ha ve already seen; that
is, we cannot deduce conclusion B directly from hypothesis A. This might happen because assuming
that A is true does not seem to give us enough information to allow us to prove that B must also be
true. In other cases, direct verification of t he conclusion B would be too time consuming or impossible
(e.g., when there might be infinitely many cases to check.). Therefore we must find another starting
point.
This goes beyond just trying ...
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Publisher Resources

ISBN: 9780123822178