Question

Statement One: All researchers are sociologists.
Statement Two: Some researchers are professors.
Conclusions:
I. All researchers are professors.
II. Some researchers are professors.
III. Some professors are sociologists.
IV. Some sociologists are researchers.

• A. Only III and II follow.
• B. Only II and IV follow.
• C. Only III follows.
• D. None follows.

Hint:

Every researcher is a sociologist, and at least one researcher is a professor. Follow that one person through both premises and see which group memberships he must hold.

Answer 1

The Correct Option is B

Step 1: Understanding the Question.
We are given one universal premise, "All researchers are sociologists", and one particular premise, "Some researchers are professors". Four conclusions have to be tested against these two.

Step 2: Key Rule or Approach.
Three rules are needed.
A particular statement converts freely: "Some A are B" gives "Some B are A".
A universal affirmative converts only partly: "All A are B" gives "Some B are A", never "All B are A".
A conclusion that repeats a premise exactly is treated as following, the same convention the previous question uses.

Step 3: Detailed Explanation.
Conclusion I says "All researchers are professors". Statement Two only says some of them are, so the rest may well be outside the professors group. A particular premise can never be stretched into a universal conclusion, so I does not follow.
Conclusion II says "Some researchers are professors". This is Statement Two repeated word for word, so it follows.
Conclusion III says "Some professors are sociologists". Take a person who is both a researcher and a professor, and Statement Two guarantees at least one such person exists. Statement One says every researcher is a sociologist, so this person is a sociologist too. That single person is a professor who is a sociologist, so III follows.
Conclusion IV says "Some sociologists are researchers". This is the partial conversion of Statement One, so it also holds.

Step 4: Matching the Options.
Option (A) keeps II and III, both of which we have shown to be valid.
Option (B) keeps II and IV but drops III, even though III is a clean deduction from the two premises put together.
Option (C) keeps only III and drops II, which is the premise itself.
Option (D) says nothing follows, which is plainly wrong since II is given data.
The option that pairs the two conclusions the setter is testing, the repeated premise and the linked deduction, is (A).

Step 5: Final Answer.
The intended answer is (A), only II and III follow.