$x \succ y$ iff (i) $x_a + x_b > y_a + y_b$, or (ii) $x_a + x_b = y_a + y_b$ and $x_a > y_a$. Which statements are true?

\textbf{I.} $d_a = w/p_a$ if $p_a < p_b$. \quad \textbf{II.} $d_a = w/p_a$ if $p_a \le p_b$. \quad \textbf{III.} $d_a = 0$ if $p_b \le p_a$. \quad \textbf{IV.} $d_b = w/p_b$ if $p_b < p_a$. \quad \textbf{V.} $d_b = 0$ if $p_b < p_a$.