If a and b are each greater than x and y, which of the following must be true?
I. ab < xy
II.a + b > x + y
III. |a| + |b| > |x| + |y|
Choose the most appropriate option:
A) I only B) II only C) I and II D) I and III E) I, II and III
I. a + b &gt; x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.   II. ab &gt; xy. Not necessarily true, consider a = b = 0 and x = y = -1 --&gt; ab = 0 &lt; 1 = xy.   III. |a| + |b| &gt; |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --&gt; |a| + |b| = 0 &lt; 2 = |x| + |y|.   Answer: II only.
<result>B</result>
If a and b are each greater than x and y, which of the following must be true?
I. ab < xy
II.a + b > x + y
III. |a| + |b| > |x| + |y|