Question

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.

• A. if only conclusion I follows
• B. if only conclusion II follows
• C. if neither I nor II follows
• D. if both I and II follow

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.

Answer 1

The Correct Option is D

Step 1: Analyze Statement I
"All books are ledgers."
This statement implies that every book is a ledger, so the set of books is entirely contained within the set of ledgers.
Step 2: Analyze Statement II
"All pens are keys."
This statement implies that every pen is a key, so the set of pens is entirely contained within the set of keys.
Step 3: Analyze Statement III
"Some pens are books."
This statement implies that there is some overlap between the sets of pens and books. Therefore, some pens are also books.
Step 4: Evaluate Conclusion I
"Some ledgers are keys."
Since all books are ledgers, and some pens (which are also keys) are books, it follows that there is at least some overlap between ledgers and keys. Therefore, conclusion I is true.
Step 5: Evaluate Conclusion II
"Some keys are books."
Since some pens are both books and keys, it follows that some keys are books. Therefore, conclusion II is also true.
Step 6: Final Answer
Both conclusions I and II follow from the given statements. Final Answer: The correct answer is (d) both I and II follow.