Answer: 7, 2, 1, 5, 6, 4, 8
Step-by-step explanation:
1. Then, 3n+4=3(2k+1)+4=6k+7=2(3k+3)+1.
2. By definition of odd, there exists integer k such that n=2k+1.
N 3. Thus, if n is odd then 3n+4 is odd or by contradiction, if 3n+4 is even then n is even, .
4. Therefore, by definition of odd, 3n+4 is odd.
5. Since k is an integer, t =3k+3 is also an integer.
6. Thus, there exists an integer t such that 3n+4=2t+1.
7. Suppose n is odd.
8. Thus, if n is odd then 3n+4 is odd or by contraposition, if 3n+4 is even then n is even, .
N 9. Suppose 3n+4 is even.
N 10. By definition of odd, n=2k+1.
Right order:
7. Suppose n is odd.
2. By definition of odd, there exists integer k such that n = 2k+1.
1. Then, 3n+4 = 3(2k+1)+4 = 6k+7 = 2(3k+3)+1.
5. Since k is an integer, t = 3k+3 is also an integer.
6. Thus, there exists an integer t such that 3n+4 = 2t+1.
4. Therefore, by definition of odd, 3n+4 is odd.
8. Thus, if n is odd then 3n+4 is odd or by contraposition, if 3n+4 is even then n is even.
