In each question below, some 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 with commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows from the given statements, disregarding commonly known facts. Giveanswer-

Statements:
Only Hat is House.
Only a few Top is Hat.
Some Wall is Top.
Conclusions:
I. All Top can never be Hat.
II. Some House are not Wall.

To determine which conclusions follow logically from the given statements, we can analyze the statements step-by-step using set theory and Venn diagram concepts.

Step 1: Analyze the Statements

1. "Only Hat is House"
In syllogisms, "Only A is B" is equivalent to "All B are A", with a critical constraint: elements of B (House) cannot belong to any other category besides A (Hat). Therefore, all Houses are Hats, and House can have no overlap with Top or Wall. This means no House can ever be Wall, Top, or any other category.

2. "Only a few Top is Hat"
This statement implies two things simultaneously:
- Some Top is Hat.
- Some Top is not Hat.
This means Top can never be fully contained within Hat (i.e., "All Top are Hat" is impossible).

3. "Some Wall is Top"
This means there is an overlap between the set of Wall and the set of Top.

Step 2: Evaluate the Conclusions

Conclusion I: "All Top can never be Hat"
From Statement 2 ("Only a few Top is Hat"), we know that "Some Top is not Hat" is definitely true. Since there is always a part of Top that is outside Hat, it is impossible for all Tops to be Hats. Thus, "All Top can never be Hat" is a true statement. Therefore, Conclusion I follows.

Conclusion II: "Some House are not Wall"
From Statement 1 ("Only Hat is House"), we established that Houses can only be Hats and cannot overlap with any other set except Hat. Since House cannot overlap with Wall, we have "No House is Wall," which also implies that "Some House are not Wall" is definitely true. Therefore, Conclusion II follows.

Since both Conclusion I and Conclusion II follow, the correct option is "If both conclusions I and II follow".