Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements:

Some teachers are scientists.

All scientists are doctors.

All doctors are engineers.

Conclusions:

I. Some doctors are teachers.

II. Some engineers are teachers.

III. Some doctors are scientists.