Question

Given below are three statements and four conclusions drawn based on the statements.

Statement 1: Some engineers are writers.
Statement 2: No writer is an actor.
Statement 3: All actors are engineers. Conclusion I: Some writers are engineers.
Conclusion II: All engineers are actors.
Conclusion III: No actor is a writer.
Conclusion IV: Some actors are writers.
Which one of the following options can be logically inferred?

• A. Only conclusion I is correct
• B. Only conclusion II and conclusion III are correct
• C. Only conclusion I and conclusion III are correct
• D. Either conclusion III or conclusion IV is correct

Hint:

When dealing with logical reasoning, always remember to assess each statement and conclusion independently and use the given facts to make deductions. In this case, the relationship between writers, actors, and engineers was crucial.

Answer 1

The Correct Option is C

Step 1: Analyzing the Statements and Conclusions.
Statement 1: Some engineers are writers. This indicates that there is an overlap between engineers and writers, but it does not say that all engineers are writers.
Statement 2: No writer is an actor. This tells us that the sets of writers and actors do not overlap.
Statement 3: All actors are engineers. This means that every actor is also an engineer.

Step 2: Analyzing Conclusion I: Some writers are engineers.
From Statement 1, we know that some engineers are writers. Therefore, it is logically correct that some writers are engineers. Thus, Conclusion I is correct.

Step 3: Analyzing Conclusion II: All engineers are actors.
Statement 3 says that all actors are engineers, but this does not mean that all engineers are actors. Therefore, Conclusion II is incorrect.

Step 4: Analyzing Conclusion III: No actor is a writer.
Statement 2 tells us that no writer is an actor. Since all actors are engineers (Statement 3), no actor can be a writer. Hence, Conclusion III is correct.

Step 5: Analyzing Conclusion IV: Some actors are writers.
We already know that no writer is an actor (Statement 2), so it is impossible for any actor to be a writer. Therefore, Conclusion IV is incorrect.

Step 6: Conclusion.
From the analysis above, Conclusion I and Conclusion III are correct. Hence, the correct answer is (C).