[Section 3.2, Problem 19] Consider the following proposition along with the included proof of the proposition:**Proposition:** For all integers $ m $ and $ n $, if $ mn $ is an even integer, then $ m $ is even or $ n $ is even.**Proof:** For either $ m $ or $ n $ to be even, there exists an integer $ k $ such that $ m = 2k $ or $ n = 2k $. So if we multiply $ m $ and $ n $, the product will contain a factor of 2 and, hence, $ mn $ will be even. □Please decide if this proposition (i) is false and the proof is incorrect; (ii) is true, but the proof is not correct; (iii) is true, the proof is correct, but the proof is not written well; or (iv) is true and the proof is correct and well-written.Please explain why you believe this. If you feel the proposition is true but the proof is not good, please write a proof of your own that is better.**Solution:**

Answered: Image /qna-images/answer/825bcc35-8cc1-45fa-9565-11c338b2bb0e.jpg

Answered: 8. [Section 3.2, Problem 19] Consider…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

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Chapter2: Second-order Linear Odes

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Question 4. Prove the following statement using its contrapositive. Let m and n be two integers. If m² + n² is divisible by 4, then both m and n are even.
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