Difficulty: Medium
Correct Answer: Only conclusion I follows
Explanation:
Introduction / Context:
This logical reasoning question works with somewhat strange category labels like books, rocks, and clips. Still, the logical structure is straightforward. You must infer what necessarily follows from the relationships described by the statements, ignoring real world meanings.
Given Data / Assumptions:
Take the following as entirely true.
Concept / Approach:
“Many books are rocks” tells us there is an overlap between the sets Books and Rocks. “All rocks are clips” places Rocks inside the set Clips. Combining these, the overlapping portion of Books and Rocks must lie inside Clips as well, giving a certain relation between Books and Clips.
Step-by-Step Solution:
Verification / Alternative check:
Draw three sets. Mark an overlapping area for Books and Rocks. Then draw the Rocks set fully inside Clips. The overlapping part of Books and Rocks lies inside Clips as well, proving that some books must be clips. This picture also shows that there certainly exist rocks that are books, so conclusion II is false.
Why Other Options Are Wrong:
Option B says only conclusion II follows, but conclusion II conflicts with the very first statement. Option C says both follow, which is impossible because the two conclusions contradict each other in light of the statements. Option D says neither follows, but we have just established that conclusion I is clearly valid.
Common Pitfalls:
Sometimes test takers are confused by the word “many” and think that the statement is vague. For logical purposes, “many” here guarantees at least “some”. That is enough to deduce conclusions about set intersections.
Final Answer:
Only conclusion I can be definitely drawn from the statements. Therefore, the correct option is “Only conclusion I follows.”
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