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.
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:
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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