Faid L.

asked • 02/12/18

Contradiction prove question, "Prove by contradiction that the difference between any odd integer and any even integer is odd"

How to do this, please help me. Thank you very much!

1 Expert Answer

By:

Andrew M. answered • 02/12/18

Tutor
New to Wyzant

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

Andrew M.

Actually, for the proof by contradiction, we first assume the opposite is true and
then show that the opposite creates a contradiction.  Thus we must try to show
that the difference between an odd integer and an even integer will be even.
 
Odd integer:  2x + 1 
Even integer:  2y
 
2x + 1 - 2y = 2x - 2y + 1 = 2(x-y) + 1
Since 2(x-y)+1 will be odd, this contradicts the assumption, and thus
shows that it is untrue.  Therefore, the difference between and odd
integer and an even integer will be odd.
Report

02/12/18

Faid L.

Ah i understand clearly, thank you Andrew M.
Report

02/12/18

Andrew M.

You're welcome Faid.  Best of luck in your endeavors.
:-)
Report

02/12/18

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.