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...

Let $m$ be odd, and let $n$ be even.


*

*An odd number $m$ is not divisible by $2$, and can be expressed in
the form $m = 2j + 1$, where $j$ is some integer.

*An even number $n$ is divisible by $2$ and can be expressed in the
form $n = 2k$, where $k$ is some integer.
Now: Subtract $n$ from $m$: express $m - n = (2j + 1) - (2k),\,$ and what is the resulting form of this difference?
