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Problem 3.3. Prove by contradiction that there exists no n e Z such that both n and n +9 are even. Hint. How to interpret the negation of "there exists no n e Z such that both n and n+ 9 are even"? Assume the negation and try to reach a contradiction.

Problem 3.3. Prove by contradiction that there exists no n e Z such that both n and n +9 are even. Hint. How to interpret the negation of "there exists no n e Z such that both n and n+ 9 are even"? Assume the negation and try to reach a contradiction.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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What I think I have so far and starting with negation is "there exist some n so that n and n+9 are both even" to find a contradiction which is 2n=n+9 => n=9 so n will never be even. Not sure if this is write or how if the explanation is correct

Problem 3.3. Prove by contradiction that there exists no n e Z such that both n and n +9 are even. Hint. How to interpret the negation of "there exists no n e Z such that both n and n+ 9 are even"? Assume the negation and try to reach a contradiction.
Transcribed Image Text:Problem 3.3. Prove by contradiction that there exists no n e Z such that both n and n +9 are even. Hint. How to interpret the negation of "there exists no n e Z such that both n and n+ 9 are even"? Assume the negation and try to reach a contradiction.
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You have written 2n=n+9, which cannot be done. Please see the proof below.

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