Directions: In the question below, some statements are given followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts.
Statements:
Only a few Novels are Classics.
All Classics are Hardcovers.
No Hardcovers are Paperbacks.
Conclusions:
I. No Novels are Paperbacks.
II. All Classics being Paperbacks is a possibility.
Correct Answer :
If neither conclusion I nor II follows
Solution :
The correct answer is If neither conclusion I nor II follows.
Step-by-Step Explanation:
1. Understanding the Given Statements:
- Only a few Novels are Classics: This implies two relations: "Some Novels are Classics" and "Some Novels are not Classics".
- All Classics are Hardcovers: The complete set of Classics is contained within the set of Hardcovers.
- No Hardcovers are Paperbacks: There is no intersection between Hardcovers and Paperbacks (they are disjoint sets).
2. Evaluating Conclusion I: No Novels are Paperbacks.
- Since all Classics are Hardcovers and no Hardcovers are Paperbacks, the portion of Novels that are Classics cannot be Paperbacks.
- However, the portion of Novels that are not Classics can potentially overlap with Paperbacks because they are not constrained to be inside Hardcovers.
- Since a possibility exists where some Novels are Paperbacks, the definite conclusion "No Novels are Paperbacks" cannot be logically deduced with certainty.
- Thus, Conclusion I does not follow.
3. Evaluating Conclusion II: All Classics being Paperbacks is a possibility.
- All Classics lie inside Hardcovers, and no Hardcovers can be Paperbacks.
- This means it is a definite fact that "No Classics are Paperbacks".
- When a definite negative relation exists between two categories, no positive possibility can exist between them.
- Thus, it is impossible for all (or any) Classics to be Paperbacks.
- Therefore, Conclusion II does not follow.
Conclusion:
Since neither conclusion I nor conclusion II logically follows, the correct option is If neither conclusion I nor II follows.
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