The least possible Venn diagram for the given statements is as below,
Conclusions: 1. Some lectures are mentors → True (It is clear from the given statement some mentor are lectures that means some lectures will also be a mentor).
2. Some professor are teachers → False (It is clear from the Venn diagram some teachers are mentors, but there is no direct relation between teachers and professors given, thus this is a false conclusion).
3. Some professors are mentor → True (It is clear from the Venn diagram, some mentor are lectures, and All lectures are professors that means some professor will also be a mentor).
Thus, Both Conclusions III and I follow.