Concept explainers
In each of 28-31: a. Rewrite the theorem in three different ways: as
and as If_________, then________(without using an explicit
universal quantifier).
b. Fill in the blanks in the proof of the theorem.
Theorm: The sum of any two odd integers is even.
Proof: Suppose m and n are any [particulasr but arbitarity chosen] odd integers.
[We must show that m+n is even.]
By (a) m+2r+1 and n=2s+1 for some integers r and s.
Theorem: The negative of any even integer is even.
Proof: Suppose n is any [particular but arbitrarily chosen] even integer
[We must show that -n is even.]
By (a) n= 2k for some integer k,
Then
Let r = —k. Then r is an integer because (— 1) and k are integers and (c)
Hence —n = 2r, where r an integer, and so -n is even by (d) [as was to be shown]
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Chapter 4 Solutions
WEBASSIGN F/EPPS DISCRETE MATHEMATICS
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
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