To prove: the sum of two odd integers is even.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:To prove: the sum of two odd integers is even.
Using the direct proof technique, we assume x and y are both odd.
The statement to be proved is a universally quantified implication.
x+y = (2m + 1) + (2n + 1) = 2 x (m+n+1).
To use the UG rule, we consider two arbitrary integers x and y.
Proof
QED
3
Using the EG/definition/UI/MP rules, x + y is even.
Using the definition/UI/MP/EI rules, we let x = 2m + 1 and y = 2n + 1, where m and n are integers.
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