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 dogs are cats.

Some cats are rats.

All rats are bats.

Conclusions :

I. Some bats are dogs.

II. Some rats are dogs.

III. Some bats are cats.