Question:medium

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.

Show 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.
Updated On: Jul 17, 2026
  • Only III and II follow.
  • Only II and IV follow.
  • Only III follows.
  • None follows.
Show Solution

The Correct Option is B

Solution and Explanation

Picture the three groups. The researchers circle sits entirely inside the sociologists circle. The professors circle cuts across the researchers circle, because only some researchers are professors. Everything else about professors is free. Test the four conclusions on that picture.

  1. Only III and II follow: II is Statement Two written out again, so it is safe. III asks whether a professor can be found who is also a sociologist. The overlap region between professors and researchers is not empty, and every point of it lies inside sociologists, so such a professor exists. Both hold.
  2. Only II and IV follow: IV is a fair reading of Statement One from the sociologists side, but this option refuses III, and III comes straight out of the overlap region described above. Rejecting a forced conclusion makes the option unsound.
  3. Only III follows: III is fine, but II is simply the given premise. Refusing it while accepting a derived statement is inconsistent.
  4. None follows: This cannot be right, because the second premise is itself one of the listed conclusions.

Conclusion I fails for a separate reason. "Some researchers are professors" leaves the remaining researchers unaccounted for, and a particular fact never grows into a universal claim.

Let's summarize:

  • An overlap that is guaranteed non empty, sitting inside a larger circle, forces a "some X are Y" link between the two outer groups.
  • Some never upgrades to all, so conclusion I is dead.
  • Among the four choices, only option (A) pairs the restated premise with the linked deduction.

The answer marked is option (A).

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