i am having trouble proving the statement below using Proof by Contrapositive. I have negated the statements as required and then i prove that $n$ is odd if and only if $7n+4$ is odd. However, from there i am stuck and am not sure how to prove the 1st part that if $n$ is negative integer, then $n$ is odd. My work is show below.
Original Statement: if n is a positive integer then n is even if and only if is 7n+4 is even. Contrapositive: If n is negative integer then n is odd if and only if 7n+4 is odd. Therefore by definition of odd: n = 2k+1 Substitute n: =7(2k+1)+4 =14k+7+4 =14k+11 =2(7k)+11 Therefore, n is odd and 7n+4 is odd.
Thats as far as i got and i dont even know if what i did above is even right though. Thanks.