The weight of three of the balls $A, B, C$ and $D$ is the same. On a balance scale with equal arms:
- when balls $A$ and $B$ are placed on the left pan and balls $C$ and $D$ are placed on the right pan, the left pan is heavier,
- when balls A and C are placed on the left pan and balls B and D are placed on the right pan, the left pan is again heavier.
Accordingly,
I. Balls A and B have equal weight.
II. Balls B and C have equal weight.
III. Ball A is heavier than ball D.
Which of the following statements are always true?
A) Only I
B) Only II
C) I and III
D) II and III
E) I, II and III