Proof (4)

' 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. '1. Thus, there exists an integert such that 3n+4=2t+1. i2. Suppose 3n+4 is even. :3. Then, 3n+4=3(2k+1)+4=6k+7=2(3k+3)+1. '4. Thus, if n is odd then 3n+4 is odd or by contradiction, if 3n+4 is even then n is even, . #5. Since k is an integer, t =3k+3 is also an integer. 6. Suppose n is odd. 7. Therefore, by definition of odd, 3n+4 is odd. 8. By definition of odd. there exists integer k such that n=2k+1. 9. Thus, if n is odd then 3n+4 is odd or by contraposition, if 3n+4 is even then n is even, . [B 10. By definition of odd. n=2k+1