Discrete Math Proofs, please help! Put the following statements into order to pr

ID: 3403851 • Letter: D

Question

Discrete Math Proofs, please help!

Put the following statements into order to prove that if 3n+4 is even then n is even. Put N next to the 3 statements that should not be used.

__ Suppose 3n+4 is even.

__ Thus, if n is odd then 3n+4 is odd or by contradiction, if 3n+4 is even then n is even, .

__ Therefore, by definition of odd, 3n+4 is odd.

__ Suppose n is odd.

__ By definition of odd, there exists integer k such that n=2k+1.

__ Then, 3n+4=3(2k+1)+4=6k+7=2(3k+3)+1.

__ Since k is an integer, t =3k+3 is also an integer.

__ Thus, there exists an integer t such that 3n+4=2t+1.

__ By definition of odd, n=2k+1.

__ Thus, if n is odd then 3n+4 is odd or by contraposition, if 3n+4 is even then n is even, .

Since answer is pretty much straight forward , let me just do the numbering :

N .........Suppose 3n+4 is even.

N .........Thus, if n is odd then 3n+4 is odd or by contradiction, if 3n+4 is even then n is even, .

6 .........Therefore, by definition of odd, 3n+4 is odd.

1 ..........Suppose n is odd.

2 ..........By definition of odd, there exists integer k such that n=2k+1.

3 ...........Then, 3n+4=3(2k+1)+4=6k+7=2(3k+3)+1.

4............ Since k is an integer, t =3k+3 is also an integer.

5............ Thus, there exists an integer t such that 3n+4=2t+1.

N .............By definition of odd, n=2k+1.

N .............Thus, if n is odd then 3n+4 is odd or by contraposition, if 3n+4 is even then n is even, .

Hope this Helps!!

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