For all numbers $a$ and $b$, let $a \heartsuit b$ be defined by $a \heartsuit b = ab + a -b$. For all numbers $x$ and $y$, which of the following must be true?

$\begin{array}{r r l} &\text{I.}\ & x \heartsuit y = y \heartsuit x\\ &\text{II.}\ & x \heartsuit y = (-y) \heartsuit (-x)\\ &\text{III.}\ & x \heartsuit y = (y+3) \heartsuit (x-3)\\ \end{array}$

(A)$\ \$ II only
(B)$\ \$ III only
(C)$\ \$ II and III only
(D)$\ \$ I, II, and III
(E)$\ \$ None of the statements