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In this logical reasoning problem, two statements about shirts and t-shirts are given, followed by two conclusions I and II. You must consider the statements to be true, even if they seem unusual, and then decide which conclusion or conclusions logically follow. Statement 1: No shirts are t-shirts. Statement 2: All t-shirts are cotton. Conclusion I: Some shirts are cotton. Conclusion II: No t-shirts are shirts. Choose the option that correctly identifies which conclusion or conclusions follow.

Difficulty: Medium

Correct Answer: Only conclusion II follows

Explanation:


Introduction / Context:
This question deals with the categories shirts, t-shirts, and cotton. Two statements define how these sets are related, and you must check which conclusions are compelled by those relations. It is essential to stay inside the information given and not rely on assumptions about real garments.


Given Data / Assumptions:
We accept these as true.

  • Statement 1: No shirts are t-shirts.
  • Statement 2: All t-shirts are cotton.
  • Conclusion I: Some shirts are cotton.
  • Conclusion II: No t-shirts are shirts.


Concept / Approach:
“No shirts are t-shirts” means the sets Shirts and T-shirts are completely disjoint. “All t-shirts are cotton” means that the entire T-shirt set lies inside the Cotton set. We check which conclusions are directly supported by these relations.


Step-by-Step Solution:

Step 1: Interpret statement 1. If no shirts are t-shirts, then any item that is a shirt cannot be a t-shirt. This also means no t-shirt is a shirt because the exclusion works both ways for the same two sets. Step 2: Thus, “No t-shirts are shirts” is simply a restatement of statement 1, using the sets in reversed order. Step 3: Statement 2 says all t-shirts are cotton, placing the T-shirt set inside the Cotton set, but it says nothing explicitly about shirts and cotton. Step 4: Conclusion I claims that “Some shirts are cotton.” For this to follow, we would need at least one shirt confirmed as cotton. The given statements do not provide any information that directly connects shirts with cotton. Step 5: Therefore, conclusion I cannot be guaranteed, while conclusion II is clearly and directly implied.


Verification / Alternative check:
Draw a Cotton set. Inside it, place the T-shirt set. Draw a Shirts set completely disjoint from the T-shirt set. Shirts may or may not intersect Cotton; the picture can be drawn both ways. Because a configuration exists where shirts have no overlap with cotton but still satisfies both statements, conclusion I is not necessary. However, in every valid drawing, the T-shirt and Shirt sets do not overlap, confirming conclusion II.


Why Other Options Are Wrong:
Option A says only conclusion I follows, which is not justified by the statements. Option C says both follow, but we have seen that conclusion I is uncertain. Option D says neither follows, but conclusion II follows directly from statement 1.


Common Pitfalls:
Students sometimes think that if all t-shirts are cotton and t-shirts are a kind of garment, then all garments (including shirts) are cotton. This is an invalid generalisation. Logical reasoning questions force you to distinguish between what is explicitly stated and what is merely possible.


Final Answer:
The only conclusion that definitely follows is conclusion II. Hence, the correct answer is “Only conclusion II follows.”

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