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:

No dog is a cat.

All cats are rats.

Conclusions:

I. No dog is a rat.

II. No rat is a dog.

III. Some rats are cats.

IV. All rats are cats.