Consider the given statements to be true and decide which of the given conclusions or assumptions can definitely be drawn from them. Statements: Many books are rocks. All rocks are clips. Conclusions: I. Some books are clips. II. No rock is a book. Choose the option that correctly identifies which conclusion or conclusions follow from the statements.

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.

  • Statement 1: Many books are rocks.
  • Statement 2: All rocks are clips.
  • Conclusion I: Some books are clips.
  • Conclusion II: No rock is a book.
  • “Many books are rocks” at least implies “Some books are rocks”.


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:

Step 1: From statement 1, we know that there are several items that are both books and rocks. So the intersection Books ∩ Rocks is non empty. Step 2: From statement 2, each rock belongs to the set Clips. So Rocks is a subset of Clips. Step 3: Any item that is in Books ∩ Rocks automatically lies in Clips as well, because it is a rock. Therefore at least some books are also clips. Step 4: This makes conclusion I, “Some books are clips,” necessarily true. Step 5: Conclusion II states, “No rock is a book.” This directly contradicts statement 1, which clearly says that many books are rocks. If many books are rocks, then at least some rocks are books, so it is impossible that no rock is a book.


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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