If an odd number is subtracted from an even number, then the remainder is odd.

Let the odd number *BC* be subtracted from the even number.

I say that the remainder *CA* is odd.

Subtract the unit *CD* from *BC,* therefore *DB* is even.

But *AB* is also even, therefore the remainder *AD* is also even. And *CD* is a unit, therefore *CA* is odd.

Therefore, *if an odd number is subtracted from an even number, then the remainder is odd.*

Q.E.D.