Faid L.

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

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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.
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02/12/18

Faid L.

Ah i understand clearly, thank you Andrew M.
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02/12/18

Andrew M.

You're welcome Faid.  Best of luck in your endeavors.
:-)
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02/12/18

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