Two 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:
All teachers are researchers.
NO researcher is unemployed.
Conclusions:
I. Some unemployed are teachers.
II. No teacher is unemployed.
III. Some teachers are unemployed.

Conclusion I : Some unemployed are teachers.

This can not be true as all teachers are researchers and no researcher is unemployed. So no teacher can be unemployed.

Conclusion 2 : No teacher is unemployed .

This statement is true and can clearly be seen from the Venn diagram.

Conclusion 3 :some teachers are unemployed.

This statement can not be true as it's contradictory to conclusion 2.

From the venn diagram it is clear that all teachers are researchers and hence neither a teacher nor a researcher can be unemployed. 

Therefore, only conclusion 2 follows.