Evaluate the following proof of the result "For any integer n, if 19n – 7 is odd, then n is even." Proposed proof: Let n be any even integer. Then n = 2k for some integer k. Consider 19n – 7 = 19(2k) – 7 = 38k – 7 = 38k – 8+1 = 2(19k – 4) + 1 Since 19k – 4 € Z, we have shown that 19n – 7 is odd.
Evaluate the following proof of the result "For any integer n, if 19n – 7 is odd, then n is even." Proposed proof: Let n be any even integer. Then n = 2k for some integer k. Consider 19n – 7 = 19(2k) – 7 = 38k – 7 = 38k – 8+1 = 2(19k – 4) + 1 Since 19k – 4 € Z, we have shown that 19n – 7 is odd.
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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Evaluate as in is there a mistake in the proof? If so show. If no mistake state result or show.
Transcribed Image Text:Evaluate the following proof of the result "For any integer n, if 19n – 7 is odd, then n is
even."
Proposed proof: Let n be any even integer. Then n = 2k for some integer k. Consider
19n – 7 = 19(2k) – 7
= 38k – 7
= 38k – 8+1
= 2(19k – 4) + 1
Since 19k – 4 € Z, we have shown that 19n – 7 is odd.
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