Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
Problem 1RQ
See similar textbooks
icon
Related questions
Question

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.
Expert Solution
Step 1

You have written 2n=n+9, which cannot be done. Please see the proof below.

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS