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

Statements:
All teachers are dancers.
All dancers are engineers.
Some engineers are beautiful.

Conclusions:
I. All teachers are beautiful.
II. Some dancers are beautiful.

Question

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

Statements:  
All teachers are dancers.  
All dancers are engineers.  
Some engineers are beautiful.

Conclusions:  
I. All teachers are beautiful.  
II. Some dancers are beautiful.

Accepted Answer

Step 1: Analyze the statements:
- All teachers are dancers (T ⊆ D).
- All dancers are engineers (D ⊆ E).
- Some engineers are beautiful (Some E are B).

From the first two statements, all teachers are dancers and all dancers are engineers, so all teachers are engineers (T ⊆ D ⊆ E).

Step 2: Analyze conclusions:  
- Conclusion I: All teachers are beautiful.
  Since only 'some engineers are beautiful' is given, it does not imply that all engineers (and hence all teachers) are beautiful. So conclusion I does not follow.

- Conclusion II: Some dancers are beautiful.  
  Since some engineers are beautiful, and dancers are a subset of engineers, it is possible that some dancers are beautiful, but it is not guaranteed. The statement 'some engineers are beautiful' does not necessarily mean that the beautiful engineers are dancers. So conclusion II does not logically follow.

Therefore, neither conclusion I nor II follows.

Answer

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