Read the given statements 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 statements.

Statements :

All bibs are hats.
Some hats are pistons.
No piston is a mat.

Conclusions : 

I. Some bibs are pistons.
II. Same mats being not hats is a possibility.
III. No bib is a piston.