In this set relation question, two statements are given about fans, cups and pillows. Treat both statements as true and decide which of the conclusions, if any, logically follow: Statements: (I) All fans are cups. (II) All cups are pillows. Conclusions: (I) All fans are pillows. (II) All pillows are fans.

Introduction / Context:
This is a straightforward syllogism problem about set inclusion. Two universal statements tell you how the sets fans, cups and pillows are nested. You must decide which of the given conclusions about fans and pillows logically follow from those nesting relations.

Given Data / Assumptions:

• Statement I: All fans are cups.
• Statement II: All cups are pillows.
• Conclusion I: All fans are pillows.
• Conclusion II: All pillows are fans.
• All refers to universal inclusion, meaning complete containment of one set in another.

Concept / Approach:
The two statements form a simple chain: fans ⊂ cups ⊂ pillows. When one set is contained inside a second, and the second is contained inside a third, then the first is also contained inside the third. This transitivity allows us to deduce whether all fans are pillows. However, we must be careful not to reverse the direction of inclusion and claim that all pillows are fans, which usually does not follow.

Step-by-Step Solution:
Step 1: From statement I, all fans are cups. So every fan lies in the set cups. Step 2: From statement II, all cups are pillows. So every cup lies in the set pillows. Step 3: Combine these: any fan is a cup, and any cup is a pillow. Therefore any fan must also be a pillow. This proves conclusion I. Step 4: Now examine conclusion II, all pillows are fans. This would mean that the set pillows is contained inside the set fans. Step 5: The statements only say that fans are a subset of cups and cups are a subset of pillows. They do not restrict pillows to be only fans; pillows could include many other things besides fans. Step 6: So conclusion II is not guaranteed by the premises.

Verification / Alternative check:
Create an example. Let fans be {f1, f2}, cups be {f1, f2, c1} and pillows be {f1, f2, c1, p1}. All fans are cups and all cups are pillows. Conclusion I holds because every fan (f1, f2) is included among the pillows. But conclusion II is false because there is a pillow p1 that is not a fan. This confirms that only conclusion I follows from the statements.

Why Other Options Are Wrong:
Option B chooses conclusion II, which reverses the set inclusion and is not implied. Option C says neither conclusion follows, ignoring the simple transitive relation that supports conclusion I. Option D claims both follow, which would require pillows and fans to be exactly the same set, something not stated. Option E suggests that exactly one of them must follow, but the exam expects you to point out specifically that it is conclusion I that follows.

Common Pitfalls:
Students often confuse all A are B with all B are A. Here, all cups are pillows does not mean all pillows are cups. Another pitfall is to read too quickly and assume that if a small set is contained in a larger one, the larger set might also be contained in the smaller one. Visualising the sets as concentric circles helps keep the direction of inclusion clear.

Final Answer:
The correct logical conclusion is that only conclusion I follows from the given statements.