Three statements are given, followed by three conclusions numbered I, II and III.
Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements:
All pencils are erasers.
All sharpeners are erasers.
All compasses are sharpeners.

Conclusions:
I. All compasses are erasers.
II. Some compasses are pencils.
III. Some erasers are compass.