In the following logical reasoning question, two statements are given, each followed by two conclusions I and II. You have to consider the statements to be true even if they seem to be at variance with commonly known facts, and then decide which conclusion or conclusions follow. Statements: (I) All shawls are carpets. (II) No carpet is a pullover. Conclusions: (I) No shawls are pullovers. (II) All carpets are shawls. Choose the option that correctly identifies which conclusion or conclusions logically follow from the statements.

Difficulty: Easy

Correct Answer: Only conclusion I follows

Explanation:


Introduction / Context:
This problem involves standard syllogistic reasoning about categories: shawls, carpets, and pullovers. You are given two universal statements about inclusion and exclusion of sets and must decide which conclusion is forced by these statements. Such questions are best understood using Venn diagram style thinking.


Given Data / Assumptions:
We accept the following statements as true.

  • Statement I: All shawls are carpets.
  • Statement II: No carpet is a pullover.
  • Conclusion I: No shawls are pullovers.
  • Conclusion II: All carpets are shawls.


Concept / Approach:
“All shawls are carpets” means the set of shawls is completely inside the set of carpets. “No carpet is a pullover” means the carpet set and pullover set do not overlap at all. We need to see what these relations imply for shawls and pullovers and for carpets and shawls.


Step-by-Step Solution:

Step 1: From statement I, every shawl is also a carpet. So the Shawl set is a subset of the Carpet set. Step 2: From statement II, there is no element that is both a carpet and a pullover. The Carpet and Pullover sets are completely disjoint. Step 3: Since every shawl is a carpet, and no carpet is a pullover, any shawl can never be a pullover. Therefore, the conclusion “No shawls are pullovers” is necessarily true. Step 4: Conclusion II claims “All carpets are shawls.” This would mean the Carpet set is equal to or contained inside the Shawl set. The statements never say that. They only say that shawls are carpets, not that every carpet must be a shawl.


Verification / Alternative check:
Draw three sets. Put the Shawl circle completely inside the Carpet circle. Then place a Pullover circle completely separate from the Carpet circle. In this diagram, no element of Shawl can reach the Pullover set, so conclusion I always holds. At the same time you can easily imagine extra carpets that are not shawls, which shows that conclusion II is not forced.


Why Other Options Are Wrong:
Option B states only conclusion II follows, which is incorrect because the data does not support “All carpets are shawls”. Option C claims neither conclusion follows, but we saw that conclusion I is solidly supported. Option D says both conclusions follow, which again fails because conclusion II is not guaranteed.


Common Pitfalls:
A common trap is to reverse the direction of “All A are B” and assume “All B are A”. Here, some learners mistakenly treat “All shawls are carpets” as if it also meant “All carpets are shawls”, which is logically invalid. Inclusion is one directional unless stated otherwise.


Final Answer:
Only conclusion I is logically valid. Therefore, the correct answer is “Only conclusion I follows.”

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