An odd integer minus an even integer is odd. Prove or Disprove: An odd integer minus an even integer is odd.
I am assuming you would define an odd integer and an even integer. than you would use quantifiers which shows your solution to be odd or even. I am unsure on how to show this...

Proof by contradiction: Let $j, k$  and $m$ are integers, suppose the difference between the even number $2j$ and odd number $2k+1 is even$, viz., $2j-(2k+1) = 2m$.  Then $2(j-k-m) = 1$.  But the right side of that equation is odd while the left side is even, which is a contradiction. QED.
