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:

Some mats are carpets.

Some carpets are blankets.

No blanket is a quilt.

Conclusions:

I. No quilt is a carpet.

II. No blanket is a mat.

III. Some carpets are mats.