If a < b < c , which of the following must be true?
(I) a < b^2
(II) a < c - b
(III) a^2 < b^2 < c^2 Choose the correct choice from the following:
A) None
B) I only
C) II only
D) III only
E) II and III
(I) a &lt; b^2. Not necessarily true fractions: try a=1/3 and b=1/2.   (II) a &lt; c-b . Not necessarily true: try a=1, b=2, and c=5/2.   (III) a^2 &lt; b^2 &lt; c^2. Not necessarily true: try a=-1, b=0, and c=1.   None of the options must be true.   Nonenswer: None.
<result>A</result>
If a < b < c , which of the following must be true?
(I) a < b^2
(II) a < c - b
(III) a^2 < b^2 < c^2