If the operation \(@\) is defined for all integers \(a\) and \(b\) by \(a@b = a + b - ab,\) which of the following state

If the operation \(@\) is defined for all integers \(a\) and \(b\) by \(a@b = a + b - ab,\) which of the following statements must be true for all integers \(a, b\) and \(c?\)

I. \(a@b = b@a\)
II. \(a@0 = a\)
III. \((a@b)@c = a@(b@c)\)

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Answer: E

Source: GMAT Prep