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


Andrew M. answered • 02/12/18

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.


Faid L.

Ah i understand clearly, thank you Andrew M.


Andrew M.

You're welcome Faid.  Best of luck in your endeavors.


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