Read the given statement(s) and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statement(s).

Statements:

Some pencils are rods.

No rod is a door.

All balls are rods.

Conclusions:

I. Some pencils being balls is a possibility.

II. No ball is a door.

III. All rods are balls.

IV. No pencil is a door.