Question

In this question, three statements followed by two conclusions numbered I and II have been given. You have to take the given statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Statements:

• Some flats are apartments.
• No apartment is a hall.
• Some halls are rooms.

Conclusions:

• [I.] At least some rooms are flats.
• [II.] No apartment is a room.

• A. Only Conclusion I is true
• B. Only Conclusion II is true
• C. Both Conclusions I and II are true
• D. Neither Conclusion I nor II is true

Hint:

In syllogism questions, only draw conclusions that are definite. If there is no direct connection between groups, the conclusion does not follow.

Answer 1

The Correct Option is D

Concept: Use logical reasoning (syllogism). Represent statements using Venn diagram relations:

• ``Some A are B'' $\Rightarrow$ Partial overlap
• ``No A is B'' $\Rightarrow$ No overlap

Step 1:Analyze the statements.}

• Some flats are apartments $\Rightarrow$ Flats $\cap$ Apartments $\neq \emptyset$
• No apartment is a hall $\Rightarrow$ Apartments $\cap$ Halls $= \emptyset$
• Some halls are rooms $\Rightarrow$ Halls $\cap$ Rooms $\neq \emptyset$

Step 2:Check Conclusion I.
“At least some rooms are flats” implies a connection between Rooms and Flats. But:

• Rooms connect with Halls
• Apartments do NOT connect with Halls
• Flats connect with Apartments

So, there is no definite link between Rooms and Flats.
\[ \Rightarrow \text{Conclusion I is false} \]
Step 3:Check Conclusion II.
“No apartment is a room” We know:

• Apartments $\cap$ Halls $= \emptyset$
• Halls $\cap$ Rooms $\neq \emptyset$

But there is no direct relation between Apartments and Rooms.
So this conclusion cannot be definitely drawn.
\[ \Rightarrow \text{Conclusion II is false} \] Final Answer: \[ {\text{Neither Conclusion I nor II is true}} \]