Question :

Directions: Some statements are given followed by four conclusions numbered I, II, III, and IV. You have to consider the statements to be true, even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statements:
All the teachers are actors.
Some actors are women.
Conclusions:
 I. All the teachers are women.
II. Some women are teachers.
III. Some women are actors.
IV. All the actors are teachers.

Option 1: Only Conclusion I follows

Option 2: Only Conclusions II and IV follow

Option 3: Only Conclusion III follows

Option 4: None of the Conclusions follows

Correct Answer: Only Conclusion III follows

Solution : The possible Venn diagram according to the given statements –

Let's analyse the conclusions –
Conclusion I: All teachers are women – From the Venn diagram, it is evident that there is no direct relation between teachers and women. So, no definite relation can be drawn between them. Therefore, this conclusion does not follow.
Conclusion II: Some women are teachers – From the Venn diagram, it is evident that there is no direct relation between teachers and women. So, no definite relation can be drawn between them. Therefore, this conclusion does not follow.
Conclusion III: Some women are actors – From the given Venn diagram, it is evident that the circles representing women and actors overlap and have a part of their area in common. So, from this, it can be concluded that some women are actors. Therefore, this conclusion follows.
Conclusion IV: All actors are teachers – From the Venn diagram, it is evident that some parts of the circle representing actors lie outside the circle representing teachers while some lie inside. So, from this, it can be concluded that some actors are teachers. Therefore, this conclusion does not follow.

Therefore, the only conclusion III is true. Hence, the third option is correct.