Define an integer k to be odd if k - 1 is even. Write up a formal proof of the following, using an indirect proof: Claim: For any natural numbers m and n, if m is odd and n is odd, then m n is even. (Notice--this is not hard to prove, but make sure that you are using a proof by contradiction. And use the official definitions of even and odd.)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 49E: Show that if the statement is assumed to be true for , then it can be proved to be true for . Is...
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Define an integer k to be odd if k - 1 is even. Write up a formal proof of the following, using
an indirect proof:
Claim: For any natural numbers m and n, if m is odd and n is odd, then m
n is even.
(Notice--this is not hard to prove, but make sure that you are using a proof by contradiction.
And use the official definitions of even and odd.)
Transcribed Image Text:Define an integer k to be odd if k - 1 is even. Write up a formal proof of the following, using an indirect proof: Claim: For any natural numbers m and n, if m is odd and n is odd, then m n is even. (Notice--this is not hard to prove, but make sure that you are using a proof by contradiction. And use the official definitions of even and odd.)
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