Problem: Which statement is correct?
Answer Choices:
A. If x<0x<0x<0, then x2>xx^{2}>xx2>x.
B. If x2>0x^{2}>0x2>0, then x>0x>0x>0.
C. If x2>xx^{2}>xx2>x, then x>0x>0x>0.
D. If x2>xx^{2}>xx2>x, then x<0x<0x<0.
E. If x<1x<1x<1, then x2<xx^{2}<xx2<x. Solution:
Since x2>0x^{2}>0x2>0 for all x≠0,x2>0>xx \neq 0, x^{2}>0>xxî€ =0,x2>0>x is true if x<0x<0x<0. Counterexamples to the other statements are easy to construct.