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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
55. Let a and b be two i nteg ers . As sume that a + b 22 and a < 11 and b < 11. Addin g u p t he last tw o
inequalities yields a + b < 22. This is clearly a contradiction. So the statement a + b 22 and a < 11
and b < 11 is false and its opposite is true.
Chapter 3: Special Kinds of Theorems
If and Only If or Equivalence Theorems
1. Part 1. Let a and b be two odd numbers. Then a = 2k +1 and b = 2t + 1, with k and t inte gers. Then
ab = (2k +1)(2t +1)= 4kt + 2k + 2t + 1 = 2(2kt + k + t) + 1. Because the number 2kt + k + t is an
integer, then ab is an odd number.
Part 2. We want to prove that if ab is an odd number, then a and b are both odd. ...
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Publisher Resources

ISBN: 9780123822178