Put the following statements into order to prove that if 3n+4 is even then n is

Question

Put the following statements into order to prove that if 3n+4 is even then n is even. Put N next to the statements that should not be used. By definition of odd, there exists integer k such that n=2k+1. Since k is an integer, t =3k+3 is also an integer. Therefore, by definition of odd, 3n+4 is odd. Then, 3n+4=3(2k+1)+4=6k+7=2(3k+3)+1. Thus, if n is odd then 3n+4 is odd or by contradiction, if 3n+4 is even then n is even, . By definition of odd, n=2k+1. Thus, there exists an integer t such that 3n+4=2t+1. Suppose n is odd. Thus, if n is odd then 3n+4 is odd or by contraposition, if 3n+4 is even then n is even, Suppose 3n+4 is even.

Explanation / Answer

We will prove the given statement by contraposition. We will use the below steps to prove the same

1. Assume n is odd.

2 Then by definition of odd, there exists k such that n= 2k+1

3 now,

3n+4

= 3(2k+1)+4

= 6k+7

= 2(3k+4) -1

So 3k+4 is 2 times an integer minus 1.

Hence 3k+4 is odd

So by contaposition if 3n+4 is even then n is even

Hence correct sequesnce are

8 1 4 9

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