Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Prove that if n is an integer and 3n+2 is even, then n is even using a proof by contraposition. Rank the options below. Then, we can write n=2k+1 for some integer k. Assume that n is odd. Then, 3n+2 = 3(2k+1) +2=6k+5=2(3k + 2) +1. This number is again of the form 2p+1 for the integer p=3k + 2; hence, it is odd. Thus, if n is odd, then 3n+2 is odd. 2 1 3 4 5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
Prove that if n is an integer and 3n+2 is even, then n is even using
a proof by contraposition.
Rank the options below.
Then, we can write n=2k+1 for some integer k.
Assume that n is odd.
Then, 3n+2 = 3(2k + 1) +2=6k+5 = 2(3k + 2) + 1.
This number is again of the form 2p + 1 for the integer p= 3k + 2; hence, it is odd.
Thus, if n is odd, then 3n+2 is odd.
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Transcribed Image Text:Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Prove that if n is an integer and 3n+2 is even, then n is even using a proof by contraposition. Rank the options below. Then, we can write n=2k+1 for some integer k. Assume that n is odd. Then, 3n+2 = 3(2k + 1) +2=6k+5 = 2(3k + 2) + 1. This number is again of the form 2p + 1 for the integer p= 3k + 2; hence, it is odd. Thus, if n is odd, then 3n+2 is odd. 2 1 3 4 5
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