Question

Statements:
All actors are performers.
Some performers are dancers.
Conclusions:
I. Some dancers are actors.
II. Some performers are actors.

• A. Only I follows
• B. Only II follows
• C. Both I and II follow
• D. Neither I nor II follows

Hint:

For syllogisms, carefully analyze sets and subsets before concluding.

Answer 1

The Correct Option is B

Step 1: Analyze Statement 1
"All actors are performers" signifies that the set of actors is a subset of the set of performers.
Step 2: Analyze Statement 2
"Some performers are dancers" indicates a partial intersection between the sets of performers and dancers.
Step 3: Evaluate Conclusion I
"Some dancers are actors" — This conclusion is not definitively established. It is possible that the sets of dancers and actors do not overlap, or that their overlap is entirely outside the group of actors who are also performers.
Step 4: Evaluate Conclusion II
"Some performers are actors" — This conclusion is valid. Since all actors are performers, it logically follows that a portion of the performers are, by definition, actors.Step 5: Final Verdict
Only Conclusion II is derivable.