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 teachers are doctors.

Some professors are doctors.

All professors are engineers.

Conclusions:

I. All professors are doctors.

II. Some doctors are engineers.

III. Some teachers are engineers.

IV. Some teachers are professors