Question 7
Nonzero real numbers $x,$ $y,$ $a,$ and $b$ satisfy $x < a$ and $y < b.$ How many of the following inequalities must be true?
**(I)** $x + y \lt a + b$
**(II)** $x - y \lt a - b$
**(III)** $xy \lt ab$
**(IV)** $\dfrac{x}{y} \lt \dfrac{a}{b}$
**(I)** $x + y \lt a + b$
**(II)** $x - y \lt a - b$
**(III)** $xy \lt ab$
**(IV)** $\dfrac{x}{y} \lt \dfrac{a}{b}$