4.29 For all real numbers $a, b, c, x, y, z$ where $x<a, y<b, z<c$, the following inequalities
I. $x y+y z+z x<a b+b c+c a$
II. $x^{2}+y^{2}+z^{2}<a^{2}+b^{2}+c^{2}$
III. $x y z<a b c$.

can be true:
(A) None of them.
(B) Only I.
(C) Only II.
(D) Only III.
(E) All of them.
(26th American High School Mathematics Examination, 1975)
[Solution] Let $x=y=z=-1, a=b=c=0$,
by $x y+y z+z x=3>0$,
and $x^{2}+y^{2}+z^{2}=3>0$, we know that inequalities (I), (II) do not always hold.
Taking $x=y=-1, \quad z=1$, and $a=b=0, c=2$, then $x y z=1>0=a b c$.
We know that (III) also does not always hold.
Therefore, the answer is $(A)$.