AMC 10 2014a Problem 7

Nonzero real numbers $x$, $y$, $a$, and $b$ satisfy $x < a$ and $y < b$. How many of the following inequalities must be true? $\textbf{(I)}\ x+y < a+b$ $\textbf{(II)}\ x-y < a-b$ $\textbf{(III)}\ xy < ab$ $\textbf{(IV)}\ \frac{x}{y} < \frac{a}{b}$ $\textbf{(A)}\ 0 \textbf{(B)}\ 1 \textbf{(C)}\ 2 \textbf{(D)}\ 3 \textbf{(E)}\ 4$