If x and y are positive integers, is x - y always positive? Explain.

No, if y happens to be a larger integer than x, then the result will be negative.

For example, lets say that x=4 and y=9, so x-y = 4-9 = - 5.

But if we were to reverse it and make x=9 and y=4, then x-y = 9-4 = 5.