If a and b are each greater than x and y, which of the following must be true?
I.|a| + |b| > |x| + |y|
II. ab > xy
III. a + b > x + y	Options:
A) I only  B) II only  C) I and II  D) III only  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: III only.
<result>D</result>
If a and b are each greater than x and y, which of the following must be true?
I.|a| + |b| > |x| + |y|
II. ab > xy
III. a + b > x + y