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...

Instead of a pure algebraic argument, which I don't dislike, it's also possible to see visually. Any even number can be represented by an array consisting of 2 x n objects, where n represents some number of objects. An odd number will be represented by a "2 by n" array with an item left over. Odd numbers don't have "evenly matched" rows or columns (depending on how you depict the array). Removing or subtracting an even number of items, then, will remove pairs of objects or items in the array. The leftover item (the "+1") will still remain and cannot have a "partner." Thus, an odd minus an even (or plus an even, for that matter) must be an odd result.
