Question

Statements:
• All professors are researchers.
• Some researchers are authors.
• No author is a politician. Which of the following conclusions definitely follows?

• A. No professor is a politician.
• B. Some researchers are not politicians.
• C. All researchers are authors.
• D. Some politicians are researchers.

Hint:

In syllogisms, a conclusion must be 100% certain. If even one alternative arrangement makes it false, the conclusion does not follow.

Answer 1

The Correct Option is B

Concept: Syllogism questions test logical deduction. A conclusion follows only if it is necessarily true based on the statements. Possibilities and assumptions are not allowed.

Step 1: Represent the statements. Statement 1: \[ \text{Professors} \subseteq \text{Researchers} \] Statement 2: \[ \text{Some Researchers} \cap \text{Authors} \neq \varnothing \] Statement 3: \[ \text{Authors} \cap \text{Politicians} = \varnothing \]

Step 2: Analyze Conclusion (A). We know professors are researchers. However, we do not know whether professors belong to the author group. Hence no definite conclusion about politicians can be made. Therefore (A) does not follow.

Step 3: Analyze Conclusion (B). Some researchers are authors. No author is a politician. Therefore those researchers who are authors cannot be politicians. Hence: \[ \text{Some Researchers are not Politicians} \] must be true. Thus conclusion (B) follows.

Step 4: Analyze Conclusion (C). The statement says: \[ \text{Some Researchers are Authors} \] not \[ \text{All Researchers are Authors} \] Hence incorrect.

Step 5: Analyze Conclusion (D). No statement establishes any politician as a researcher. Hence incorrect.

Step 6: Final conclusion. The only definite conclusion is: \[ \boxed{\text{Some Researchers are not Politicians}} \] Therefore, \[ \boxed{\text{Option (B)}} \]