Question:medium

In this question, there are three statements followed by conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follow from the three statements. 
Statements:
  • All books are ledgers.
  • All pens are keys.
  • Some pens are books.
Conclusions:
  • I. Some ledgers are keys.
  • II. Some keys are books.

Show Hint

In logical reasoning, when dealing with sets, carefully analyze the relationships between sets to determine if the conclusions follow from the given statements. Use Venn diagrams or logical reasoning rules for better clarity.
Updated On: Jan 13, 2026
  • if only conclusion I follows
  • if only conclusion II follows
  • if neither I nor II follows
  • if both I and II follow
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Analyze Statement I: "All books are ledgers."
This indicates that the set of all books is a subset of the set of all ledgers.

Step 2: Analyze Statement II: "All pens are keys."
This indicates that the set of all pens is a subset of the set of all keys.

Step 3: Analyze Statement III: "Some pens are books."
This indicates that there is an intersection between the set of pens and the set of books; some items are members of both sets.

Step 4: Evaluate Conclusion I: "Some ledgers are keys."
Given that some pens are books (Statement III), and all books are ledgers (Statement I), it follows that some pens are ledgers. Since all pens are keys (Statement II), these pens that are also ledgers must also be keys. Therefore, there is an overlap between ledgers and keys. Conclusion I is valid.

Step 5: Evaluate Conclusion II: "Some keys are books."
As established in Step 4, some pens are both books and keys. This directly implies that some keys are books. Conclusion II is valid.

Step 6: Final Answer
Both conclusions I and II are logically derived from the provided statements.



Final Answer: The correct answer is (d) both I and II follow.
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