Read the following statements and conclusions: Statements: All windows are doors. No door is a wall. Conclusions: 1. No window is a wall. 2. No wall is a door. Which of the conclusions logically follow from the given statements?

Introduction / Context:
This is a straightforward syllogism question involving three sets: windows, doors and walls. You are given one subset statement and one disjointness statement, then asked which conclusions necessarily follow. Your goal is to reason about set inclusion and exclusion using basic logic.

Given Data / Assumptions:

• Statement 1: All windows are doors. (Windows ⊆ Doors.)

• Statement 2: No door is a wall. (Doors and walls are disjoint sets.)

• Conclusion 1: No window is a wall.

• Conclusion 2: No wall is a door.

Concept / Approach:
We use simple set logic. If every window is also a door, and no door belongs to the set of walls, then windows cannot belong to the set of walls either. Additionally, "No door is a wall" is logically equivalent to "No wall is a door", because the lack of overlap is symmetric. We will formalise this reasoning step by step.

Step-by-Step Solution:
Step 1: Translate the first statement: All windows are doors ⇒ every element of the set Windows is also in the set Doors. Step 2: Translate the second statement: No door is a wall ⇒ the intersection of Doors and Walls is empty; there is no element that is both a door and a wall. Step 3: Test Conclusion 1: "No window is a wall." Since all windows are doors and no door is a wall, if any window were a wall, it would automatically be a door and a wall at the same time, which is forbidden by Statement 2. Hence, no window can be a wall. Conclusion 1 follows. Step 4: Test Conclusion 2: "No wall is a door." The statement "No door is a wall" means there is no object that is both a door and a wall. Because the relation "no A is B" is symmetric, we can also say "no wall is a door." So Conclusion 2 also follows directly. Step 5: Therefore, both conclusions 1 and 2 are correct consequences of the given statements.

Verification / Alternative check:
Draw three circles representing Windows, Doors and Walls. Place the Windows circle entirely inside the Doors circle, since all windows are doors. Then place the Walls circle completely separate from the Doors circle, since no door is a wall. You will see immediately that the Windows circle does not intersect the Walls circle, and that the Doors and Walls circles do not overlap at all in either direction. This visual check confirms both conclusions.

Why Other Options Are Wrong:
Option A and Option B each claim that only one conclusion follows, but we have shown that both follow. Option C claims that only one of them can follow, which is untrue because both express the same core disjointness in slightly different language. Option D is therefore the only accurate choice.

Common Pitfalls:
Students sometimes overlook the symmetry of negative categorical statements and treat "No A is B" and "No B is A" as different. Others fail to consider how subset relationships interact with disjointness, forgetting that if a bigger set is disjoint from another, all its subsets are also disjoint from that other set.

Final Answer:
Both conclusions logically follow, so the correct choice is that both conclusions 1 and 2 follow.