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. Give answer-

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. Give answer-

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.

The correct answer is: If both conclusions I and II follow.

Let us carefully analyze the given statements and draw a Venn diagram–style logical picture to evaluate each conclusion.

Given Statements:
1. Only Hat is House.
2. Only a few Top is Hat.
3. Some Wall is Top.

Interpreting the Statements:

Statement 1 — "Only Hat is House":
This means all Houses are Hats, but not all Hats are Houses. In other words, the set "House" is entirely contained within the set "Hat". There are elements in Hat that are NOT in House.

Statement 2 — "Only a few Top is Hat":
This means only a few (some) Tops are Hats. So the overlap between Top and Hat is partial — some Tops are Hats, but many Tops are NOT Hats. Crucially, it also implies that NOT all Tops can be Hats, since only "a few" are.

Statement 3 — "Some Wall is Top":
This means there is a partial overlap between Wall and Top — some Walls are Tops, but not necessarily all.

Now let us evaluate each conclusion:

Conclusion I — "All Top can never be Hat":
From Statement 2, "Only a few Top is Hat" — this directly tells us that it is impossible for ALL Tops to be Hats. The word "only a few" explicitly restricts the Tops-inside-Hat to a small portion, meaning a definite portion of Top always lies outside Hat. Therefore, it is definitively true that All Top can never be Hat.
✅ Conclusion I follows.

Conclusion II — "Some House are not Wall":
From Statement 1: All Houses are Hats (House ⊆ Hat).
From Statement 2: Only a few Tops are Hats — meaning most of Hat is not overlapping with Top at all.
From Statement 3: Some Walls are Tops — meaning Wall only partially intersects Top.

Now, since Wall intersects only with Top (partially), and the Houses lie within Hat — and the part of Hat that intersects with Top is only "a few", while most of House lies in the part of Hat that does NOT touch Top or Wall — it follows that at least some Houses are definitely not Wall. The part of the Hat (and House) that lies outside the Top-Hat intersection is never touched by Wall at all. Therefore, those Houses are certainly not Wall.
✅ Conclusion II follows.

Final Verdict:
Both Conclusion I and Conclusion II logically follow from the given statements.
The correct answer is: If both conclusions I and II follow.