Question

Two statements are given, followed by four options about which conclusions follow. Decide which conclusions logically follow the statements.
Statements:
(i) Some democracies are dictatorships.
(ii) No dictatorship is a monarchy.
Conclusions:
I. No democracy is a monarchy.
II. No dictatorship is a democracy.
III. Some democracies are monarchies.
IV. Some dictatorships are democracies.

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

Hint:

When a statement says “Some $A$ are $B$,” that exact conclusion always follows. Universal negations like “No $A$ are $C$” apply only to $A$ and $C$ unless there is an explicit link to other sets.

Answer 1

The Correct Option is B

Let $D=$ democracies,\ $K=$ dictatorships,\ $M=$ monarchies.
From (i): Some $D$ are $K$ \;($D\cap K\neq \varnothing$).
From (ii): No $K$ is $M$ \;($K\cap M=\varnothing$).
I. No democracy is a monarchy — Not implied, since $D$ outside $K$ could still be $M$. Hence, does not follow.
II. No dictatorship is a democracy — Contradicts (i) which says some $K$ are $D$. Hence, does not follow.
III. Some democracies are monarchies — Not given; cannot be concluded from the premises. Hence, does not follow.
IV. Some dictatorships are democracies — This is exactly statement (i). Hence, follows.
Thus, only IV follows - option (b).