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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 4,1-2: The sum of any even integer and jjiv odd integer u odd.
Proof: Suppose m la any even integer and n is
__(a)__By definition of even. m-2r for some
(b) and by definition of odd, n = 2s + 1 for
some integer s. By subsitution and slgebra.
Since r and s are both integers, so is their nun r + s. Hence m + n has the form twice some integer plus one and so (d)__by definition of odd.
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Chapter 4 Solutions
Discrete Mathematics With Applications
- 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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