Question

In the questions given below, two statements are given followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the statements. Statement: All windows are doors. No door is wall.
Conclusions:
I. No window is wall.
II. No wall is door.

• A. Only conclusion I follows.
• B. Only conclusion II follows.
• C. Neither conclusion I nor II follows.
• D. Both conclusion I and II follow.

Hint:

In syllogism, if "All A are B" and "No B is C", then automatically "No A is C". Also, "No A is B" implies "No B is A".

Answer 1

The Correct Option is D

Concept: This is a syllogism problem. We use Venn diagram or logical relation method:
• "All A are B" means A is completely inside B.
• "No B is C" means B and C do not overlap.

Step 1: Interpret the first statement. \[ \text{All windows are doors} \] This means: \[ \text{Windows} \subset \text{Doors} \]

Step 2: Interpret the second statement. \[ \text{No door is wall} \] This means: \[ \text{Doors} \cap \text{Walls} = \emptyset \]

Step 3: Analyze Conclusion I. \[ \text{No window is wall} \] Since all windows are inside doors, and doors have no overlap with walls, it follows that windows also cannot overlap with walls. Thus, Conclusion I is true.

Step 4: Analyze Conclusion II. \[ \text{No wall is door} \] Given: \[ \text{No door is wall} \] This is a mutually exclusive relationship, meaning: \[ \text{No wall is door} \] Thus, Conclusion II is also true.

Step 5: Final conclusion. Both conclusions logically follow from the given statements. \[ \boxed{\text{Both I and II follow}} \]