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Reading Section 1.6-1.8 Problem Prove the following theorem: Theorem Vn E Z, n is either even or odd (but not both). Your proof must address the following points: 1. n is even or odd (and nothing else). 2. n is odd = n is not even (hint: contradiction). 3. n is even → n is not odd (hint: contrapositive). The first point is a bit more difficult. Start by making a statement about 0. Then assuming that n is even, what can you say about n – 1 and n + 1? Likewise, assuming that n is odd, what can - 1 and n + 1. Can you organize these facts into an argument that shows that you say about n you have accounted for all possible n E Z?

Reading Section 1.6-1.8 Problem Prove the following theorem: Theorem Vn E Z, n is either even or odd (but not both). Your proof must address the following points: 1. n is even or odd (and nothing else). 2. n is odd = n is not even (hint: contradiction). 3. n is even → n is not odd (hint: contrapositive). The first point is a bit more difficult. Start by making a statement about 0. Then assuming that n is even, what can you say about n – 1 and n + 1? Likewise, assuming that n is odd, what can - 1 and n + 1. Can you organize these facts into an argument that shows that you say about n you have accounted for all possible n E Z?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Reading Section 1.6-1.8 Problem Prove the following theorem: Theorem Vn E Z, n is either even or odd (but not both). Your proof must address the following points: 1. n is even or odd (and nothing else). 2. n is odd = n is not even (hint: contradiction). 3. n is even → n is not odd (hint: contrapositive). The first point is a bit more difficult. Start by making a statement about 0. Then assuming that n is even, what can you say about n – 1 and n + 1? Likewise, assuming that n is odd, what can - 1 and n + 1. Can you organize these facts into an argument that shows that you say about n you have accounted for all possible n E Z?
Transcribed Image Text:Reading Section 1.6-1.8 Problem Prove the following theorem: Theorem Vn E Z, n is either even or odd (but not both). Your proof must address the following points: 1. n is even or odd (and nothing else). 2. n is odd = n is not even (hint: contradiction). 3. n is even → n is not odd (hint: contrapositive). The first point is a bit more difficult. Start by making a statement about 0. Then assuming that n is even, what can you say about n – 1 and n + 1? Likewise, assuming that n is odd, what can - 1 and n + 1. Can you organize these facts into an argument that shows that you say about n you have accounted for all possible n E Z?
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