Define a binary operation on Z, the set of integers, by the equation m • n = m + n + mn. Which of
the following statements is (are) true about the binary structure (Z, • )?
I. This structure is not a group since the operation is not associative.
II. This structure is not a group since there is no identity element.
III. This structure is not a group since not all elements have an inverse.
IV. This structure is a group.
(A)I and II only (B)I and III only (C)II and III only (D)III only
D