Difficulty: Hard
Correct Answer: Neither conclusion I nor conclusion II follows
Explanation:
Introduction / Context:
This question extends standard syllogism reasoning by adding more sets and multiple universal negative statements. You must judge two conclusions that refer to possibility and combined membership across sets. The objective is to strictly follow the given relationships and see whether any diagram can satisfy both the statements and the conclusions. A conclusion fails if it violates even one of the premise relationships in every possible arrangement.
Given Data / Assumptions:
Concept / Approach:
The main tools are subset and disjoint set reasoning. Statements like “All papers are books” mean the papers set lies completely inside the books set. “No stationary item is a book” means stationary items and books are disjoint. To test a possibility conclusion, you must look for at least one Venn diagram that satisfies all premises and also satisfies the conclusion. If such a diagram cannot be drawn because the conclusion always conflicts with the premises, then that conclusion does not follow.
Step-by-Step Solution:
Step 1: Translate the first two statements:
Step 2: Translate the next two statements:
Step 3: Evaluate Conclusion I: “Some papers are stationary items is a possibility.” If some papers were stationary items, that would mean the intersection of Papers and Stationary is non empty. But all papers are books, and stationary items are disjoint from books. If an element lies in both Papers and Stationary, it would lie in Books (because all papers are books) and also in Stationary, which contradicts “No stationary item is a book.”
Step 4: Because any overlap between Papers and Stationary would violate the rule that Stationary and Books are disjoint, there is no diagram where some papers are stationary items. Therefore, Conclusion I is not a valid possibility.
Step 5: Now examine Conclusion II: “Some pens are books as well as papers.” For an object to be a paper and a book, it must be in the Papers subset, which lies inside Books. The conclusion also says that this object is a pen.
Step 6: However, we must also respect “No paper is a pencil” and “All pencils are pens.” Nothing directly forbids some pens from being books or papers, but we must check for conflicts. If a paper is also a pen, that paper is not a pencil (by the third statement). There is no direct contradiction here, so at first glance it may seem possible.
Step 7: Look more carefully. The given statements do not guarantee that any pen overlaps with books or papers at all. Pens might form a completely separate set from books. Because a conclusion in standard syllogism must follow in every valid arrangement, we must test if there is a valid diagram where no pen is a book or paper.
Step 8: Construct such a diagram: place Papers inside Books, and Stationary outside Books. Place Pencils inside Pens, and then place the entire Pens set completely outside the Books set. This satisfies:
In this arrangement, there is no pen that is also a book or a paper. Therefore, it is not necessary that some pens are books and papers.
Verification / Alternative check:
The key is to distinguish “can be” from “must be”. The premises allow pens to be totally separate from books, so we cannot insist that some pens are books and papers. That makes Conclusion II not logically necessary. Meanwhile, any attempt to make some papers stationary items immediately creates an element lying in both Books and Stationary, which contradicts the given “No stationary item is a book.” This shows that Conclusion I is also impossible. Hence neither conclusion follows from the premises.
Why Other Options Are Wrong:
Option a: “Only conclusion I follows” is false because Conclusion I contradicts the disjointness of Stationary and Books.
Option b: “Only conclusion II follows” is wrong because we have shown a valid model where no pen is a book, so the existence of a pen that is also a paper is not required.
Option c: “Either conclusion I or conclusion II follows” is incorrect since both can fail simultaneously in the same diagram.
Option e: “Both conclusion I and conclusion II follow” is clearly false for the same reasons.
Common Pitfalls:
Students often confuse logical necessity with mere plausibility. Just because it seems natural that pens, books, and papers might overlap in everyday life does not mean the premises force that overlap. Another mistake is overlooking how one universal negative (no stationary item is a book) interacts with a universal positive (all papers are books), which together completely forbid any paper from being stationary. Always check for hidden contradictions that arise when you try to enforce a possibility conclusion.
Final Answer:
Neither conclusion I nor conclusion II follows.
Discussion & Comments