Question

Statement One: Some democracies are dictatorship.
Statement Two: No dictatorship is a monarchy.
Conclusions:
I. No democracy is a monarchy.
II. No dictatorship is a democracy.
III. Some democracies are monarchy.
IV. Some dictatorships are democracies.

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

Hint:

Only a slice of the democracies group is known to be dictatorship. Ask what that slice looks like when you read it from the dictatorship side, and whether the rest of the democracies group is bound by anything at all.

Answer 1

The Correct Option is B

Step 1: Understanding the Question.
The first premise is particular affirmative: some democracies are dictatorships. The second is universal negative: no dictatorship is a monarchy. Four conclusions have to be checked.

Step 2: Key Rule or Approach.
A particular affirmative converts freely, so "Some A are B" always gives "Some B are A".
A particular premise combined with a negative premise can give at most a particular negative conclusion of the form "Some A are not B". It can never give a universal conclusion, and it can never give an affirmative link.

Step 3: Detailed Explanation.
Conclusion I says "No democracy is a monarchy". The premises only tell us about the part of the democracies group that is made of dictatorships. That part is cut off from monarchies. The rest of the democracies group is untouched and may sit inside monarchies. So I is not forced.
Conclusion II says "No dictatorship is a democracy". This directly contradicts the first premise, which says some democracies are dictatorships. A conclusion cannot deny its own premise, so II fails.
Conclusion III says "Some democracies are monarchy". This is only a possibility, never a certainty. Nothing in the premises builds a link from democracies to monarchies, so III fails.
Conclusion IV says "Some dictatorships are democracies". This is the conversion of Statement One and it is always valid, so IV follows.

Step 4: Checking the Wrong Options.
Option (A) says none follows, but IV is a straight conversion of the first premise, so this is wrong.
Option (C) pairs II and III, and both have already been ruled out.
Option (D) pairs I and IV. IV is fine, but I over reaches from a part of the democracies group to the whole of it.
The conclusion that does follow but is not listed is "Some democracies are not monarchies", which is the proper particular negative from these two premises.

Step 5: Final Answer.
Only conclusion IV follows, so the answer is (B).